A120209 -id:A120209

A120134

a(n) = 4 + floor(Sum_{k=1..n-1} a(k) / 2).

+10
13

4, 6, 9, 13, 20, 30, 45, 67, 101, 151, 227, 340, 510, 765, 1148, 1722, 2583, 3874, 5811, 8717, 13075, 19613, 29419, 44129, 66193, 99290, 148935, 223402, 335103, 502655, 753982, 1130973, 1696460, 2544690, 3817035, 5725552, 8588328, 12882492

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

FORMULA

a(n) ~ c * (3/2)^n, where c = 3.9320886310283094862025842648411406926537121258867950257873967568454133192... - Vaclav Kotesovec, May 07 2023

MAPLE

a := proc(n) option remember; 4 + iquo(add(a(k), k = 1..n-1), 2) end:

seq(a(n), n = 1..37); # Peter Luschny, May 07 2023

MATHEMATICA

f[s_]:= Append[s, 4+Floor[Plus @@ s/2]]; Nest[f, {4}, 37] (* Robert G. Wilson v, Jun 10 2006 *)

PROG

(SageMath)

@CachedFunction

def A120134(n): return 4 + sum(A120134(k) for k in range(1, n))//2

print([A120134(n) for n in range(1, 41)]) # G. C. Greubel, May 07 2023

CROSSREFS

Cf. A073941, A072493, A112088, A120135 - A120209, A172161.

KEYWORD

nonn

AUTHOR

Graeme McRae, Jun 10 2006

EXTENSIONS

Name edited by Peter Luschny, May 07 2023

STATUS

approved

A120135

a(n) = 5 + floor((1 + Sum_{j=1..n-1} a(j)) / 2).

+10
3

5, 8, 12, 18, 27, 40, 60, 90, 135, 203, 304, 456, 684, 1026, 1539, 2309, 3463, 5195, 7792, 11688, 17532, 26298, 39447, 59171, 88756, 133134, 199701, 299552, 449328, 673992, 1010988, 1516482, 2274723, 3412084, 5118126, 7677189, 11515784

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

FORMULA

a(n) ~ c * (3/2)^n, where c = 3.514931952760438754899508881646642282344325354834703833076259269449577... - Vaclav Kotesovec, May 07 2023

MATHEMATICA

a[n_]:= a[n]= 5 +Floor[(1+Sum[a[k], {k, n-1}])/2];

Table[a[n], {n, 60}] (* G. C. Greubel, May 07 2023 *)

PROG

(SageMath)

@CachedFunction

def A120135(n): return 5 + (1 + sum(A120135(k) for k in range(1, n)))//2

[A120135(n) for n in range(1, 61)] # G. C. Greubel, May 07 2023

CROSSREFS

Cf. A073941, A072493, A112088, A120134, A120136 - A120209.

KEYWORD

nonn

AUTHOR

Graeme McRae, Jun 10 2006

STATUS

approved

A120136

a(n) = 7 + floor(Sum_{j=1..n-1} a(j) / 2).

+10
3

7, 10, 15, 23, 34, 51, 77, 115, 173, 259, 389, 583, 875, 1312, 1968, 2952, 4428, 6642, 9963, 14945, 22417, 33626, 50439, 75658, 113487, 170231, 255346, 383019, 574529, 861793, 1292690, 1939035, 2908552, 4362828, 6544242, 9816363, 14724545

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

MATHEMATICA

nxt[{t_, a_}] := Module[{c=7+Floor[t/2]}, {t+c, c}];

NestList[nxt, {7, 7}, 40][[All, 2]] (* Harvey P. Dale, Jan 13 2017 *)

PROG

(SageMath)

@CachedFunction

def A120136(n): return 7 +sum(A120136(k) for k in range(1, n))//2

[A120136(n) for n in range(1, 60)] # G. C. Greubel, May 08 2023

CROSSREFS

Cf. A073941, A072493, A112088, A120134, A120135, A120137 - A120209.

KEYWORD

nonn

AUTHOR

Graeme McRae, Jun 10 2006

STATUS

approved

A120137

a(n) = 8 + floor( (1 + Sum_{j=1..n-1} a(j)) / 2).

+10
3

8, 12, 18, 27, 41, 61, 92, 138, 207, 310, 465, 698, 1047, 1570, 2355, 3533, 5299, 7949, 11923, 17885, 26827, 40241, 60361, 90542, 135813, 203719, 305579, 458368, 687552, 1031328, 1546992, 2320488, 3480732, 5221098, 7831647, 11747471, 17621206

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

MATHEMATICA

a[n_]:= a[n]= 8 +Floor[(1 +Sum[a[k], {k, n-1}])/2];

Table[a[n], {n, 60}] (* G. C. Greubel, May 08 2023 *)

nxt[{t_, a_}]:=Module[{c=8+Floor[(1+t)/2]}, {t+c, c}]; NestList[nxt, {8, 8}, 40][[;; , 2]] (* Harvey P. Dale, Sep 10 2023 *)

PROG

(SageMath)

@CachedFunction

def A120137(n): return 8 +(1 +sum(A120137(k) for k in range(1, n)))//2

[A120137(n) for n in range(1, 60)] # G. C. Greubel, May 08 2023

CROSSREFS

Cf. A073941, A072493, A112088, A120134 - A120136, A120138 - A120209.

KEYWORD

nonn

AUTHOR

Graeme McRae, Jun 10 2006

STATUS

approved

A120138

a(n) = 10 + floor(Sum_{j=1..n-1} a(j) / 2).

+10
3

10, 15, 22, 33, 50, 75, 112, 168, 252, 378, 567, 851, 1276, 1914, 2871, 4307, 6460, 9690, 14535, 21803, 32704, 49056, 73584, 110376, 165564, 248346, 372519, 558779, 838168, 1257252, 1885878, 2828817, 4243226, 6364839, 9547258, 14320887

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

MATHEMATICA

a[n_]:= a[n]= 10 +Quotient[Sum[a[k], {k, n-1}], 2];

Table[a[n], {n, 60}] (* G. C. Greubel, May 08 2023 *)

PROG

(SageMath)

@CachedFunction

def A120138(n): return 10 +sum(A120138(k) for k in range(1, n))//2

[A120138(n) for n in range(1, 60)] # G. C. Greubel, May 08 2023

CROSSREFS

Cf. A073941, A072493, A112088, A120134 - A120137, A120139 - A120209.

KEYWORD

nonn

AUTHOR

Graeme McRae, Jun 10 2006

STATUS

approved

A120139

a(n) = 11 + floor( (1 + Sum_{j=1..n-1} a(j)) / 2).

+10
3

11, 17, 25, 38, 57, 85, 128, 192, 288, 432, 648, 972, 1458, 2187, 3280, 4920, 7380, 11070, 16605, 24908, 37362, 56043, 84064, 126096, 189144, 283716, 425574, 638361, 957542, 1436313, 2154469, 3231704, 4847556, 7271334, 10907001, 16360501

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

MATHEMATICA

a[n_]:= a[n]= 11 +Quotient[1 + Sum[a[k], {k, n-1}], 2];

Table[a[n], {n, 60}] (* G. C. Greubel, May 08 2023 *)

PROG

(SageMath)

@CachedFunction

def A120139(n): return 11 +(1 +sum(A120139(k) for k in range(1, n)))//2

[A120139(n) for n in range(1, 60)] # G. C. Greubel, May 08 2023

CROSSREFS

Cf. A073941, A072493, A112088, A120134 - A120138, A120140 - A120209.

KEYWORD

nonn

AUTHOR

Graeme McRae, Jun 10 2006

STATUS

approved

A120140

a(n) = 13 + floor(Sum_{j=1..n-1} a(j)/2).

+10
3

13, 19, 29, 43, 65, 97, 146, 219, 328, 492, 738, 1107, 1661, 2491, 3737, 5605, 8408, 12612, 18918, 28377, 42565, 63848, 95772, 143658, 215487, 323230, 484845, 727268, 1090902, 1636353, 2454529, 3681794, 5522691, 8284036, 12426054, 18639081

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

MATHEMATICA

a[n_]:= a[n]= 13 +Quotient[Sum[a[k], {k, n-1}], 2];

Table[a[n], {n, 60}] (* G. C. Greubel, May 11 2023 *)

PROG

(SageMath)

@CachedFunction

def A120140(n): return 13 + sum(A120140(k) for k in range(1, n))//2

[A120140(n) for n in range(1, 60)] # G. C. Greubel, May 11 2023

CROSSREFS

Cf. A073941, A072493, A112088, A120134 - A120139, A120141 - A120209.

KEYWORD

nonn

AUTHOR

Graeme McRae, Jun 10 2006

STATUS

approved

A120141

a(n) = 14 + floor( (1 + Sum_{j=0..n-1} a(j)) / 2).

+10
3

14, 21, 32, 48, 72, 108, 162, 243, 364, 546, 819, 1229, 1843, 2765, 4147, 6221, 9331, 13997, 20995, 31493, 47239, 70859, 106288, 159432, 239148, 358722, 538083, 807125, 1210687, 1816031, 2724046, 4086069, 6129104, 9193656, 13790484

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

MATHEMATICA

nxt[{t_, a_}]:=Module[{a2=14+Floor[(1+t)/2]}, {t+a2, a2}]; NestList[nxt, {0, 14}, 60][[All, 2]]//Rest (* Harvey P. Dale, Nov 28 2018 *)

PROG

(SageMath)

@CachedFunction

def A120141(n): return 14 +(1 +sum(A120141(k) for k in range(1, n)))//2

[A120141(n) for n in range(1, 60)] # G. C. Greubel, May 11 2023

CROSSREFS

Cf. A073941, A072493, A112088, A120134 - A120140, A120142 - A120209.

KEYWORD

nonn

AUTHOR

Graeme McRae, Jun 10 2006

STATUS

approved

A120142

a(n) = 16 + floor(Sum_{j=1..n-1} a(j)/2).

+10
3

16, 24, 36, 54, 81, 121, 182, 273, 409, 614, 921, 1381, 2072, 3108, 4662, 6993, 10489, 15734, 23601, 35401, 53102, 79653, 119479, 179219, 268828, 403242, 604863, 907295, 1360942, 2041413, 3062120, 4593180, 6889770, 10334655, 15501982

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

MATHEMATICA

Nest[Append[#, 16+Floor[Total[#]/2]]&, {16}, 40] (* Harvey P. Dale, Apr 20 2011 *)

PROG

(SageMath)

@CachedFunction

def A120142(n): return 16 + (sum(A120142(k) for k in range(1, n)))//2

[A120142(n) for n in range(1, 60)] # G. C. Greubel, May 11 2023

CROSSREFS

Cf. A073941, A072493, A112088, A120134 - A120141, A120143 - A120209.

KEYWORD

nonn

AUTHOR

Graeme McRae, Jun 10 2006

STATUS

approved

A120143

a(n) = 17 + floor( (1 + Sum_{j=0..n-1} a(j))/2 ).

+10
3

17, 26, 39, 58, 87, 131, 196, 294, 441, 662, 993, 1489, 2234, 3351, 5026, 7539, 11309, 16963, 25445, 38167, 57251, 85876, 128814, 193221, 289832, 434748, 652122, 978183, 1467274, 2200911, 3301367, 4952050, 7428075, 11142113, 16713169

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

MATHEMATICA

nxt[{t_, a_}]:=Module[{c=17+Floor[(1+t)/2]}, {t+c, c}]; NestList[nxt, {17, 17}, 60][[All, 2]] (* Harvey P. Dale, Dec 25 2020 *)

PROG

(SageMath)

@CachedFunction

def A120143(n): return 17 + (1 +sum(A120143(k) for k in range(1, n)))//2

[A120143(n) for n in range(1, 60)] # G. C. Greubel, May 11 2023

CROSSREFS

Cf. A073941, A072493, A112088, A120134 - A120142, A120144 - A120209.

KEYWORD

nonn

AUTHOR

Graeme McRae, Jun 10 2006

STATUS

approved