A069476 -id:A069476

Search: a069476 -id:a069476

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A069473

First differences of (n+1)^6-n^6 (A022522).

+10
4

62, 602, 2702, 8162, 19502, 39962, 73502, 124802, 199262, 303002, 442862, 626402, 861902, 1158362, 1525502, 1973762, 2514302, 3159002, 3920462, 4812002, 5847662, 7042202, 8411102, 9970562, 11737502, 13729562, 15965102, 18463202

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

OFFSET

0,1

LINKS

Table of n, a(n) for n=0..27.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

a(n) = 30*n^4 + 120*n^3 + 210*n^2 + 180*n + 62.

G.f.: 2*(31 + 146*x + 156*x^2 + 26*x^3 + x^4)/(1 - x)^5. [Bruno Berselli, Feb 25 2015]

MATHEMATICA

Differences[Table[(n + 1)^6 - n^6, {n, 0, 30}]] (* Harvey P. Dale, Dec 27 2011 *)

PROG

(Magma) [30*n^4+120*n^3+210*n^2+180*n+62: n in [0..30]]; // Bruno Berselli, Feb 25 2015

CROSSREFS

Cf. A001014, A022522, A069474, A069475, A069476, A068236.

KEYWORD

nonn,easy

AUTHOR

Eli McGowan (ejmcgowa(AT)mail.lakeheadu.ca), Mar 26 2002

EXTENSIONS

Offset changed from 1 to 0 and added a(0)=62 by Bruno Berselli, Feb 25 2015

STATUS

approved

A069474

First differences of A069473.

+10
3

540, 2100, 5460, 11340, 20460, 33540, 51300, 74460, 103740, 139860, 183540, 235500, 296460, 367140, 448260, 540540, 644700, 761460, 891540, 1035660, 1194540, 1368900, 1559460, 1766940, 1992060, 2235540, 2498100, 2780460, 3083340

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

OFFSET

0,1

LINKS

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = 120*n^3 + 540*n^2 + 900*n + 540.

G.f.: 60*(9 - x + 5*x^2 - x^3)/(1 - x)^4. [Bruno Berselli, Feb 25 2015]

MATHEMATICA

Differences[Table[(n + 1)^6 - n^6, {n, 0, 30}], 2] (* Harvey P. Dale, Dec 27 2011 *)

CROSSREFS

Cf. A001014, A022522, A069473, A069475, A069476.

Equals 60 * A005898(n+1).

KEYWORD

nonn,easy

AUTHOR

Eli McGowan (ejmcgowa(AT)mail.lakeheadu.ca), Mar 26 2002

EXTENSIONS

Offset changed from 1 to 0 and added a(0)=540 by Bruno Berselli, Feb 25 2015

STATUS

approved

A069475

First differences of A069474, successive differences of (n+1)^6-n^6.

+10
3

1560, 3360, 5880, 9120, 13080, 17760, 23160, 29280, 36120, 43680, 51960, 60960, 70680, 81120, 92280, 104160, 116760, 130080, 144120, 158880, 174360, 190560, 207480, 225120, 243480, 262560, 282360, 302880, 324120, 346080, 368760, 392160, 416280

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

OFFSET

0,1

LINKS

Table of n, a(n) for n=0..32.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = 360*n^2 + 1440*n + 1560 = 120*A056107(n+2).

G.f.: 120*(13 - 11*x + 4*x^2)/(1 - x)^3. - Bruno Berselli, Feb 25 2015

MATHEMATICA

Table[360 n^2 + 1440 n + 1560, {n, 0, 40}] (* Bruno Berselli, Feb 25 2015 *)

PROG

(PARI) a(n)=360*n^2+1440*n+1560 \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. A001014, A022522, A056107, A069473, A069474, A069476.

KEYWORD

nonn,easy

AUTHOR

Eli McGowan (ejmcgowa(AT)mail.lakeheadu.ca), Mar 26 2002

EXTENSIONS

Offset changed from 1 to 0 and added a(0)=1560 by Bruno Berselli, Feb 25 2015

STATUS

approved

A140801

a(0)=360, a(n)=a(n-1)+720 for n>=1.

+10
0

360, 1080, 1800, 2520, 3240, 3960, 4680, 5400, 6120, 6840, 7560, 8280, 9000, 9720, 10440, 11160, 11880, 12600, 13320, 14040, 14760, 15480, 16200, 16920, 17640, 18360, 19080, 19800, 20520, 21240, 21960, 22680, 23400, 24120, 24840, 25560, 26280, 27000, 27720, 28440, 29160

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

OFFSET

0,1

LINKS

Table of n, a(n) for n=0..40.

FORMULA

a(n) = 360+720*n

MATHEMATICA

NestList[720+#&, 360, 40] (* or *) 720*Range[0, 40]+360 (* Harvey P. Dale, Jan 24 2017 *)

CROSSREFS

A069476 (same sequence, starting with 2520).

KEYWORD

nonn,easy,less

AUTHOR

Paul Curtz, Jul 15 2008

STATUS

approved

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