A028901 -id:A028901

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A081597

Let n = 10*x + y where 0 <= y <= 9, x >= 0. Then a(n) = 6*x + y.

+10
2

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 42, 43, 44, 45, 46, 47

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

OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

FORMULA

G.f.: -x*(3*x^9 -x^8 -x^7 -x^6 -x^5 -x^4 -x^3 -x^2 -x -1) / ((x -1)^2*(x +1)*(x^4 -x^3 +x^2 -x +1)*(x^4 +x^3 +x^2 +x +1)). - Colin Barker, Jun 24 2014

a(n) = n - 4*floor(n/10). [Bruno Berselli, Jun 24 2014]

a(n) = a(n-1) + a(n-10) - a(n-11) for n > 10. - Chai Wah Wu, Apr 25 2017

MAPLE

A081597:=n->n-4*floor(n/10): seq(A081597(n), n=0..150); # Wesley Ivan Hurt, Apr 25 2017

MATHEMATICA

CoefficientList[Series[-x (3 x^9 - x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x - 1)/((x - 1)^2 (x + 1) (x^4 - x^3 + x^2 - x + 1) (x^4 + x^3 + x^2 + x + 1)), {x, 0, 150}], x] (* Vincenzo Librandi, Jun 25 2014 *)

PROG

(PARI) my(n, x, y); vector(200, n, y=(n-1)%10; x=(n-1-y)\10; 6*x+y) \\ Colin Barker, Jun 24 2014

(Magma) k:=6; [n-(10-k)*Floor(n/10): n in [0..10]]; // Bruno Berselli, Jun 24 2014

CROSSREFS

Cf. A081502. Different from A028901.

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Apr 22 2003

STATUS

approved

A083291

Triangular array read by rows: T(n,k) = k*floor(n/10) + n mod 10, 0<=k<=n.

+10
2

0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 3, 4, 5, 6, 7, 8, 9, 10, 11

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

OFFSET

0,4

COMMENTS

A010879(n)=T(n,0);

A076314(0)=T(0,0), A076314(n)=T(n,1) for n>0;

A028897(n)=T(n,n) for n<=1, A028897(n)=T(n,2) for n>1;

A028898(n)=T(n,n) for n<=2, A028898(n)=T(n,3) for n>2;

A028899(n)=T(n,n) for n<=3, A028899(n)=T(n,4) for n>3;

A028900(n)=T(n,n) for n<=4, A028900(n)=T(n,5) for n>4;

A028901(n)=T(n,n) for n<=5, A028901(n)=T(n,6) for n>5;

A028902(n)=T(n,n) for n<=6, A028902(n)=T(n,7) for n>6;

A028903(n)=T(n,n) for n<=7, A028903(n)=T(n,8) for n>7;

A028904(n)=T(n,n) for n<=8, A028904(n)=T(n,9) for n>8;

T(n,n) = n for n<=9, T(n,10) = n for n>9;

A083292(n) = T(n,n).

LINKS

Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of the triangle, flattened).

EXAMPLE

From Paolo Xausa, May 22 2024: (Start)

Triangle begins:

[0] 0;

[1] 1, 1;

[2] 2, 2, 2;

[3] 3, 3, 3, 3;

[4] 4, 4, 4, 4, 4;

[5] 5, 5, 5, 5, 5, 5;

[6] 6, 6, 6, 6, 6, 6, 6;

[7] 7, 7, 7, 7, 7, 7, 7, 7;

[8] 8, 8, 8, 8, 8, 8, 8, 8, 8;

[9] 9, 9, 9, 9, 9, 9, 9, 9, 9, 9;

[10] 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10;

... (End)

MATHEMATICA

Table[k*Floor[n/10] + Mod[n, 10], {n, 0, 10}, {k, 0, n}]//Flatten (* Paolo Xausa, May 22 2024 *)

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller, Apr 23 2003

EXTENSIONS

Offset changed to 0 by Paolo Xausa, May 22 2024

STATUS

approved

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