A008615 -id:A008615 - cp's OEIS frontend

A008616 Expansion of 1/((1-x^2)(1-x^5)).

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

Offset: 0

N. J. A. Sloane

Number of partitions of n into parts of size two and five.

It appears that, for n >= 2, a(n-2) is also (1) the number of partitions of 3n that are 6-term arithmetic progressions and (2) floor(n/2) - floor(2n/5). - John W. Layman, Jun 29 2009

G. E. Andrews, K. Eriksson, Integer Partitions, Cambridge Univ. Press, 2004. page 30, Exercise 48.
D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 100.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 213
M. Janjic, On Linear Recurrence Equations Arising from Compositions of Positive Integers, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.7.
Index entries for two-way infinite sequences
Index entries for linear recurrences with constant coefficients, signature (0, 1, 0, 0, 1, 0, -1).

Cf. A000217, A025810.

Cf. A008615. - John W. Layman, Jun 29 2009

m:=100; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x^2)*(1-x^5)))); // Wesley Ivan Hurt, Dec 27 2021

CoefficientList[Series[1 / ((1 - x^2) (1 - x^5)),{x, 0, 100}], x] (* Vincenzo Librandi, Jun 21 2013 *)

{a(n) = if( n<-6, -a(-7 - n), polcoeff( 1 / (1 - x^2) / (1 - x^5) + x * O(x^n), n))} /* Michael Somos, Jan 25 2005 */

a(n) = floor(n/10+(3+(-1)^n)/4) \\ Charles R Greathouse IV, Jun 19 2013

G.f.: 1/((1-x^2)(1-x^5)) = 1/((x-1)^2*(1+x)*(1+x+x^2+x^3+x^4)).
Euler transform of finite sequence [0, 1, 0, 0, 1].
a(n) = -a(-7 - n) = a(n - 10) + 1 = a(n - 2) + a(n - 5) - a(n - 7). - Michael Somos, Jan 25 2005
A000217(a(n)) = A025810(n). - Michael Somos, Dec 15 2002
a(n) = 7/20 + n/10 + (-1)^n/4 + (A105384(n) + 2*(A010891(n) + A105384(n+4)))/5. - R. J. Mathar, Jun 28 2009
a(n) = floor(n/10 + (3 + (-1)^n)/4). - Tani Akinari, Jun 20 2013

A165027 Number of n-digit fixed points under the base-4 Kaprekar map A165012.

Original entry on oeis.org

1, 0, 1, 1, 0, 3, 1, 3, 3, 5, 3, 8, 5, 9, 8, 12, 9, 16, 12, 18, 16, 22, 18, 27, 22, 30, 27, 35, 30, 41, 35, 45, 41, 51, 45, 58, 51, 63, 58, 70, 63, 78, 70, 84, 78, 92, 84, 101, 92, 108, 101, 117, 108, 127, 117, 135, 127, 145, 135, 156, 145, 165, 156, 176, 165, 188, 176, 198

Offset: 1

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n=1..200
Index entries for the Kaprekar map

Cf. A165012, A165016, A165025, A165026.

In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A008615 (base 3), A008617 (base 5), A165066 (base 6), A008722 (base 7, conjecturally), A165105 (base 8), A165125 (base 9), A164733 (base 10).

Conjectures from Chai Wah Wu, Apr 13 2024: (Start)
a(n) = 2*a(n-2) + a(n-3) - a(n-4) - 2*a(n-5) + a(n-7) for n > 8.
G.f.: x*(x^7 - x^6 - 2*x^5 + x^4 + x^2 - 1)/((x - 1)^3*(x + 1)^2*(x^2 + x + 1)). (End)

A165066 Number of n-digit fixed points under the base-6 Kaprekar map A165051.

Original entry on oeis.org

1, 0, 1, 0, 1, 3, 0, 2, 1, 4, 2, 3, 2, 5, 4, 5, 3, 8, 4, 8, 6, 9, 7, 10, 8, 13, 9, 13, 10, 17, 12, 16, 14, 19, 16, 21, 16, 24, 19, 25, 21, 28, 23, 29, 26, 33, 27, 35, 29, 39, 33, 39, 35, 44, 38, 46, 40, 50, 43, 53, 46, 56, 50, 58, 53, 64, 55, 66, 59, 71, 63, 73, 66, 78, 71, 81, 73, 87

Offset: 1

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n=1..100
Index entries for the Kaprekar map

Cf. A165051, A165055, A165064, A165065.

In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A008615 (base 3), A165027 (base 4), A008617 (base 5), A008722 (base 7, conjecturally), A165105 (base 8), A165125 (base 9), A164733 (base 10).

Conjectures from Chai Wah Wu, Apr 13 2024: (Start)
a(n) = - a(n-1) + a(n-3) + 2*a(n-4) + 2*a(n-5) + a(n-6) - a(n-7) - 2*a(n-8) - 2*a(n-9) - a(n-10) + a(n-12) + a(n-13) for n > 15.
G.f.: x*(-x^14 + x^8 - x^5 + x^4 - x^2 - x - 1)/((x - 1)^3*(x + 1)^2*(x^2 + 1)*(x^2 + x + 1)*(x^4 + x^3 + x^2 + x + 1)). (End)

A025795 Expansion of 1/((1-x^2)(1-x^3)(1-x^5)).

Original entry on oeis.org

1, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 9, 11, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 21, 23, 24, 25, 27, 28, 29, 31, 32, 34, 35, 37, 38, 40, 42, 43, 45, 47, 48, 51, 52, 54, 56, 58, 60, 62, 64, 66, 68, 71, 72, 75, 77, 79, 82, 84, 86, 89, 91, 94, 96, 99, 101, 104

Offset: 0

N. J. A. Sloane

a(n) is the number of ways to pay n dollars with coins of two, three and five dollars. E.g., a(0)=1 because there is one way to pay: with no coin; a(1)=0 no possibility; a(2)=1 (2=1*2); a(3)=1 (3=1*3); a(4)=1 (4=2*2) a(5)=2 (5=3+2=1*5) ... - Richard Choulet, Jan 20 2008

a(n) is the number of partitions of n into parts 2, 3, and 5. See the preceding comment by R. Choulet. - Wolfdieter Lang, Mar 15 2012

			G.f. = 1 + x^2 + x^3 + x^4 + 2*x^5 + 2*x^6 + 2*x^7 + 3*x^8 + 3*x^9 + 4*x^10 + ...

Alois P. Heinz, Table of n, a(n) for n = 0..10000
Milan Janjic, On Linear Recurrence Equations Arising from Compositions of Positive Integers, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.7.
Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,0,0,-1,-1,0,1).

Cf. A008676, A078495, A103221.

a[ n_] := Quotient[n^2 + 10 n + 1 - 13 Mod[n, 2], 60] + 1; (* Michael Somos, Nov 17 2017 *)

{a(n) = (n^2 + 10*n + 1 - n%2 * 13) \60 + 1} /* Michael Somos, Feb 05 2008 */

G.f.: 1/((1-x^2)*(1-x^3)*(1-x^5)).
Let [b(1); b(2); ...; b(p)] denote a periodic sequence: e.g., [0; 1] defines the sequence c such that c(0)=c(2)=...=c(2*k)=0 and c(1)=c(3)=...=c(2*k+1)=1. Then a(n)=0.25*[0; 1] - (1/3)*[1; 0; 0] + (1/5)*[0; 1; 1; 0; 3] + ((n+1)*(n+2)/60) + (7*(n+1)/60). - Richard Choulet, Jan 20 2008
If ||A|| is the nearest number to A (A not a half-integer) we also have a(n) = ||((n+1)*(n+9)/60) + (1/5)[0; 1; 1; 0; 3]. - Richard Choulet, Jan 20 2008
a(n) = 77/360 + 7*(n+1)/60 + (n+2)*(n+1)/60 + (-1)^n/8 - (2/9)*cos(2*(n+2)*Pi/3) + (4/(5*sqrt(5)+25))*cos(2*n*Pi/5) - (4/(5*sqrt(5)-25))*cos(4*n*Pi/5). - Richard Choulet, Jan 20 2008
Euler transform of length 5 sequence [0, 1, 1, 0, 1]. - Michael Somos, Feb 05 2008
a(n) = a(-10-n) for all n in Z. - Michael Somos, Feb 25 2008
a(n) - a(n-2) = A008676(n). a(n) - a(n-5) = A103221(n) = A008615(n+2). A078495(n) = 2^(a(n-7) + a(n-9)) * 3^a(n-8) for all n in Z. - Michael Somos, Nov 17 2017, corrected Jun 23 2021
a(n)-a(n-3) = A008616(n). - R. J. Mathar, Jun 23 2021
a(n) = floor((n^2 + 10*n + 6*(9+(-1)^n))/60). - Hoang Xuan Thanh, Jun 15 2025

A165105 Number of n-digit fixed points under the base-8 Kaprekar map A165090.

Original entry on oeis.org

1, 1, 1, 0, 0, 2, 1, 1, 1, 1, 0, 4, 0, 4, 2, 2, 2, 4, 2, 3, 6, 5, 2, 7, 2, 6, 5, 10, 5, 8, 5, 8, 7, 9, 11, 12, 7, 11, 9, 12, 9, 21, 10, 14, 12, 15, 13, 18, 20, 18, 15, 20, 15, 23, 16, 30, 20, 23, 20, 26, 21, 27, 32, 29, 23, 32, 25, 32, 28, 43

Offset: 1

Joseph Myers, Sep 04 2009

Index entries for the Kaprekar map

Cf. A165090, A165094, A165103, A165104.

In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A008615 (base 3), A165027 (base 4), A008617 (base 5), A165066 (base 6), A008722 (base 7, conjecturally), A165125 (base 9), A164733 (base 10).

Conjectures from Chai Wah Wu, Apr 13 2024: (Start)
a(n) = - a(n-1) + a(n-3) + 2*a(n-4) + 2*a(n-5) + a(n-6) - a(n-7) - 2*a(n-8) - 2*a(n-9) - a(n-10) + a(n-12) + a(n-13) for n > 15.
G.f.: x*(-x^14 + x^8 - x^5 + x^4 - x^2 - x - 1)/((x - 1)^3*(x + 1)^2*(x^2 + 1)*(x^2 + x + 1)*(x^4 + x^3 + x^2 + x + 1)). (End)

A165125 Number of n-digit fixed points under the base-9 Kaprekar map A165110.

Original entry on oeis.org

1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 2, 1, 1, 2, 2, 3, 2, 2, 1, 4, 2, 3, 2, 3, 3, 4, 2, 3, 4, 4, 4, 4, 4, 4, 5, 4, 4, 5, 4, 5, 5, 5, 5, 6, 5, 6, 6, 6, 5, 7, 6, 7, 6, 6, 6, 8, 6, 7, 7, 8, 8, 8, 7, 7, 9, 8, 8

Offset: 1

Joseph Myers, Sep 04 2009

Index entries for the Kaprekar map

Cf. A165110, A165114, A165123, A165124.

In other bases: A004526 (base 2, adjusted to start 1, 0, 0, 1, 1, ...), A008615 (base 3), A165027 (base 4), A008617 (base 5), A165066 (base 6), A008722 (base 7, conjecturally), A165105 (base 8), A164733 (base 10).

Conjectures from Chai Wah Wu, Apr 13 2024: (Start)
a(n) = a(n-2) - a(n-3) + a(n-5) - a(n-6) + a(n-8) + a(n-15) - a(n-17) + a(n-18) - a(n-20) + a(n-21) - a(n-23) for n > 24.
G.f.: x*(x^23 + x^22 - x^21 + x^20 + 2*x^19 - x^18 + x^17 + 3*x^16 - 2*x^15 + 3*x^13 - x^12 + 2*x^10 - x^9 + 2*x^7 - x^5 + x^4 + x^3 - x^2 + 1)/(x^23 - x^21 + x^20 - x^18 + x^17 - x^15 - x^8 + x^6 - x^5 + x^3 - x^2 + 1). (End)

A321201 Irregular triangle T with the nontrivial solutions of 2e2 + 3e3 = n, for n >= 2, with nonnegative e2 and e3, ordered as pairs with increasing e2 values.

Original entry on oeis.org

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

Offset: 2

Wolfdieter Lang, Nov 05 2018

The length of row n is 2*A(n), with A(n) = A008615(n+2) for n >= 2: 2*[1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2, 3, 3, 3, 3, 4, 3, 4, ...].
The trivial solution for n = 0 is [0, 0]. There is no solution for n = 1.
The row sums are given in A321202.
If a partition of n with parts 2 or 3 (with inclusive or) is written as 2^{e2} 3^{e3}, where e2 and e3 are nonnegative numbers, then in row n, all pairs [e2, e3] are given, for n >= 2, ordered with increasing values of e2.
The corresponding irregular triangle with the multinomial numbers n!/((n - (e2 + e3))!*e2!*e3!) is given in A321203. It gives the coefficients of x^n = x^{2*{e2} + 3*{e3}} of (1 + x^2 + x^3)^n, for n >= 2.

			The triangle T(n, k) begins (pairs are separated by commas):
  n\k  0  1   2  3   4  5   6  7 ...
  2:   1  0
  3:   0  1
  4:   2  0
  5:   1  1
  6:   0  2,  3  0
  7:   2  1
  8:   1  2,  4  0
  9:   0  3,  3  1
  10:  2  2,  5  0
  11:  1  3,  4  1
  12:  0  4,  3  2,  6  0
  13:  2  3,  5  1,
  14:  1  4,  4  2,  7  0
  15:  0  5,  3  3,  6  1
  16:  2  4,  5  2,  8  0
  17:  1  5,  4  3,  7  1
  18:  0  6,  3  4,  6  2,  9  0
  19:  2  5,  5  3,  8  1
  20:  1  6,  4  4,  7  2, 10  0
  ...
n=8: the two solutions of 2*e2 + 3*e3 = 8 are [e2, e3] = [1, 2] and = [4, 0], and 1 < 4, therefore row 8 is 1  2  4  0, with a comma after the first pair.

Cf. A008615, A321202, A321203.

row[n_] := Reap[Do[If[2 e2 + 3 e3 == n, Sow[{e2, e3}]], {e2, 0, n/2}, {e3, 0, n/3}]][[2, 1]];
Table[row[n], {n, 2, 20}] // Flatten (* Jean-François Alcover, Nov 23 2018 *)

T(n, k) gives all pairs [e2, e3] solving 2*e2 + 3*e3 = n, ordered with increasing value of e2, for n >= 2. The trivial solution [0, 0] for n = 0 is not recorded. There is no solution for n = 1.

Missing row 2 inserted by Jean-François Alcover, Nov 23 2018

A060548 a(n) is the number of D3-symmetric patterns that may be formed with a top-down equilateral triangular arrangement of closely packed black and white cells satisfying the local matching rule of Pascal's triangle modulo 2, where n is the number of cells in each edge of the arrangement. The matching rule is such that any elementary top-down triangle of three neighboring cells in the arrangement contains either one or three white cells.

Original entry on oeis.org

2, 1, 2, 2, 2, 2, 4, 2, 4, 4, 4, 4, 8, 4, 8, 8, 8, 8, 16, 8, 16, 16, 16, 16, 32, 16, 32, 32, 32, 32, 64, 32, 64, 64, 64, 64, 128, 64, 128, 128, 128, 128, 256, 128, 256, 256, 256, 256, 512, 256, 512, 512, 512, 512, 1024, 512, 1024, 1024, 1024, 1024, 2048, 1024, 2048

Offset: 1

André Barbé (Andre.Barbe(AT)esat.kuleuven.ac.be), Apr 02 2001

Harry J. Smith, Table of n, a(n) for n = 1..500
André Barbé, Symmetric patterns in the cellular automaton that generates Pascal's triangle modulo 2, Discr. Appl. Math. 105 (2000), 1-38.
Index entries for sequences related to cellular automata.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,2).

Cf. A008611, A008615.

a[n_] := a[n] = a[n-2]*a[n-3]/a[n-5]; a[1] = a[3] = a[4] = a[5] = 2; a[2] = 1; Table[a[n], {n, 1, 63}] (* Jean-François Alcover, Dec 27 2011, after second formula *)
LinearRecurrence[{0,0,0,0,0,2},{2,1,2,2,2,2},70] (* Harvey P. Dale, Sep 19 2016 *)

PARI
```
a(n)=if(n<1,0,2^((n+3)\6+(n%6==1)))
```

a(n) = 2^A008615(n+1) = 2^floor(A008611(n+2)/2) for n >= 1.
a(n) = 2^(floor((n+3)/6) + d(n)), where d(n)=1 if n mod 6=1, else d(n)=0.
a(n) = a(n-2)*a(n-3)/a(n-5), n>5.
From Colin Barker, Aug 29 2013: (Start)
a(n) = 2*a(n-6) for n>1.
G.f.: -x*(2*x^5+2*x^4+2*x^3+2*x^2+x+2) / (2*x^6-1). (End)
Sum_{n>=1} 1/a(n) = 7. - Amiram Eldar, Dec 10 2022

A260708 a(2n) = n(2n+1), a(2n+7) = a(2n+1) + 12*n + 28, with a(1)=1, a(3)=6, a(5)=16.

Original entry on oeis.org

0, 1, 3, 6, 10, 16, 21, 29, 36, 46, 55, 68, 78, 93, 105, 122, 136, 156, 171, 193, 210, 234, 253, 280, 300, 329, 351, 382, 406, 440, 465, 501, 528, 566, 595, 636, 666, 709, 741, 786, 820, 868, 903, 953, 990, 1042, 1081, 1136, 1176, 1233, 1275, 1334, 1378

Offset: 0

Paul Curtz, Nov 17 2015

Conjecture: this sequence is 0 followed by A264041.
After 3, if a(n) is prime then n == 1 (mod 6).
a(n) is a square for n = 0, 1, 5, 8, 145, 288, 1777, 6533, 9800, 168097, 332928, 2051425, 7539845, ...

			a(0) = 0*1 = 0,
a(1) = 1,
a(2) = 1*3 = 3,
a(3) = 6,
a(4) = 2*5 = 10,
a(5) = 16,
a(6) = 3*7 = 21,
a(7) = a(1) +12*0 +28 = 29, etc.

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,0,1,-1,-1,1).

Cf. A000217, A008615, A014105, A260160, A260699, A264041.

LinearRecurrence[{1, 1, -1, 0, 0, 1, -1, -1, 1}, {0, 1, 3, 6, 10, 16, 21, 29, 36}, 50] (* Bruno Berselli, Nov 18 2015 *)

concat(0, Vec(-x*(x^6+x^5+3*x^4+2*x^3+2*x^2+2*x+1)/((x-1)^3*(x+1)^2*(x^2-x+1)*(x^2+x+1)) + O(x^100))) \\ Colin Barker, Nov 18 2015

[n*(n+1)/2+(1-(-1)^n)*floor(n/6+1/3)/2 for n in (0..60)] # Bruno Berselli, Nov 18 2015

From Colin Barker, Nov 17 2015: (Start)
G.f.: x*(1 + 2*x + 2*x^2 + 2*x^3 + 3*x^4 + x^5 + x^6) / ((1 - x)^3*(1 + x)^2*(1 - x + x^2)*(1 + x + x^2)).
a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-6) - a(n-7) - a(n-8) + a(n-9) for n>8. (End)
a(2*k)   = A000217(2*k) by definition; for odd indices:
a(6*k+1) = 18*k^2 + 10*k + 1,
a(6*k+3) = 2*(9*k^2 + 11*k + 3),
a(6*k+5) = 2*(k + 1)*(9*k + 8), that is A178574.
a(n) = A260699(n) + A008615(n).
a(n) = n*(n + 1)/2 + (1 - (-1)^n)*floor(n/6 + 1/3)/2. [Bruno Berselli, Nov 18 2015]

Edited by Bruno Berselli, Nov 18 2015

A029143 Expansion of 1/((1-x^2)(1-x^3)(1-x^5)*(1-x^6)). Molien series for u.g.g.r. #31 of order 46080. Poincaré series [or Poincare series] for ring of even weight Siegel modular forms of genus 2.

Original entry on oeis.org

1, 0, 1, 1, 1, 2, 3, 2, 4, 4, 5, 6, 8, 7, 10, 11, 12, 14, 17, 16, 21, 22, 24, 27, 31, 31, 37, 39, 42, 46, 52, 52, 60, 63, 67, 73, 80, 81, 91, 95, 101, 108, 117, 119, 131, 137, 144, 153, 164, 167, 182, 189, 198, 209, 222

Offset: 0

N. J. A. Sloane

a(k) for k>0 is the dimension of the space of Siegel modular forms of genus 2 and weight 2k (for the full modular group Gamma_2). Also: Number of solutions of 4x+6y+10z+12w=k in nonnegative integers x,y,z,w. - Kilian Kilger (kilian(AT)nihilnovi.de), Sep 26 2009

Number of partitions of n into parts 2, 3, 5, and 6. - Joerg Arndt, Jun 21 2014

H. Klingen, Intro. lectures on Siegel modular forms, Cambridge, p. 123, Corollary.
L. Smith, Polynomial Invariants of Finite Groups, Peters, 1995, p. 199 (No. 31).

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Vincenzo Librandi)
W. C. Huffman, The biweight enumerator of self-orthogonal binary codes, Discr. Math. Vol. 26 1979, pp. 129-143.
J. Igusa, On Siegel modular forms of genus 2, Amer. J. Math., 84 (1962), 175-200.
Index entries for Molien series
Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,0,1,-1,-2,-1,1,0,0,1,1,0,-1).

Cf. A027640 for the dimension of even and odd weight Siegel modular forms. See A165684 (resp. A165685) for the corresponding space of cusp forms. - Kilian Kilger (kilian(AT)nihilnovi.de), Sep 26 2009

M := Matrix(16, (i,j)-> if (i=j-1) or (j=1 and member(i, [2, 3, 6, 10, 13, 14])) then 1 elif j=1 and member(i, [7, 9, 16]) then -1 elif j=1 and i=8 then -2 else 0 fi): a:= n -> (M^(n))[1,1]: seq(a(n), n=0..54); # Alois P. Heinz, Jul 25 2008

CoefficientList[Series[1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^6)),{x,0,54}],x] (* Jean-François Alcover, Mar 20 2011 *)
LinearRecurrence[{0,1,1,0,0,1,-1,-2,-1,1,0,0,1,1,0,-1},{1,0,1,1,1,2,3,2,4,4,5,6,8,7,10,11},60] (* Harvey P. Dale, May 12 2015 *)

a(n) = A165684(n) + A008615(n+2). - Kilian Kilger (kilian(AT)nihilnovi.de), Sep 26 2009
a(n) ~ 1/1080*n^3. - Ralf Stephan, Apr 29 2014
a(0)=1, a(1)=0, a(2)=1, a(3)=1, a(4)=1, a(5)=2, a(6)=3, a(7)=2, a(8)=4, a(9)=4, a(10)=5, a(11)=6, a(12)=8, a(13)=7, a(14)=10, a(15)=11, a(n)= a(n-2)+ a(n-3)+a(n-6)-a(n-7)- 2*a(n-8)-a(n-9)+a(n-10)+a(n-13)+ a(n-14)- a(n-16). - Harvey P. Dale, May 12 2015

Definition corrected by Kilian Kilger (kilian(AT)nihilnovi.de), Sep 25 2009

cp's OEIS Frontend

A008616 Expansion of 1/((1-x^2)(1-x^5)).

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A165027 Number of n-digit fixed points under the base-4 Kaprekar map A165012.

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A165066 Number of n-digit fixed points under the base-6 Kaprekar map A165051.

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A025795 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^5)).

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A165105 Number of n-digit fixed points under the base-8 Kaprekar map A165090.

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A165125 Number of n-digit fixed points under the base-9 Kaprekar map A165110.

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A321201 Irregular triangle T with the nontrivial solutions of 2*e2 + 3*e3 = n, for n >= 2, with nonnegative e2 and e3, ordered as pairs with increasing e2 values.

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A260708 a(2n) = n*(2*n+1), a(2n+7) = a(2n+1) + 12*n + 28, with a(1)=1, a(3)=6, a(5)=16.

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A025795 Expansion of 1/((1-x^2)(1-x^3)(1-x^5)).

A321201 Irregular triangle T with the nontrivial solutions of 2e2 + 3e3 = n, for n >= 2, with nonnegative e2 and e3, ordered as pairs with increasing e2 values.

A260708 a(2n) = n(2n+1), a(2n+7) = a(2n+1) + 12*n + 28, with a(1)=1, a(3)=6, a(5)=16.

A029143 Expansion of 1/((1-x^2)(1-x^3)(1-x^5)*(1-x^6)). Molien series for u.g.g.r. #31 of order 46080. Poincaré series [or Poincare series] for ring of even weight Siegel modular forms of genus 2.