A025810 Expansion of 1/((1-x^2)(1-x^5)(1-x^10)) in powers of x.

1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 3, 3, 3, 3, 3, 3, 6, 3, 6, 3, 6, 6, 6, 6, 6, 6, 10, 6, 10, 6, 10, 10, 10, 10, 10, 10, 15, 10, 15, 10, 15, 15, 15, 15, 15, 15, 21, 15, 21, 15, 21, 21, 21, 21, 21, 21, 28, 21, 28, 21, 28, 28, 28, 28, 28, 28, 36, 28, 36, 28, 36, 36, 36, 36, 36, 36

Offset

0,11

Comments

Number of partitions of n into parts of size 2, 5, and 10.

a(n) is always a triangular number.

Links

Table of n, a(n) for n=0..79.

Index entries for linear recurrences with constant coefficients, signature (0, 1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, -1, 0, 1).

Formula

G.f.: 1/((1-x^2)(1-x^5)(1-x^10)).

Euler transform of length 10 sequence [ 0, 1, 0, 0, 1, 0, 0, 0, 0, 1]. - Michael Somos, Mar 18 2012

a(n) = a(-17 - n) = a(n - 10) + A008616(n) for all n in Z. - Michael Somos, Mar 18 2012

a(n) = A000217( A008616(n) ) = A000008(n) - A000008(n - 1). - Michael Somos, Dec 15 2002

Example

G.f. = 1 + x^2 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + 3*x^10 + x^11 + 3*x^12 + ...

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^5)(1-x^10)), {x, 0, 85}], x]  (* Harvey P. Dale, Apr 06 2011 *)
a[ n_] := Module[ {m = Mod[n, 10], k}, k = n - m; If[ m == 1 || m == 3, k -= 10]; k (k + 30) / 200 + 1]; (* Michael Somos, Aug 16 2016 *)

Prog

(PARI) {a(n) = if( n<-16, a(-17 - n), polcoeff( 1 / ((1 - x^2) * (1 - x^5) * (1 - x^10)) + x * O(x^n), n))}; /* Michael Somos, Mar 18 2012 */
(PARI) {a(n) = my(m = n%10); n -= m; if( m==1 || m==3, n -= 10); n * (n + 30) / 200 + 1}; /* Michael Somos, Aug 16 2016 */

Crossrefs

Cf. A000008, A000217, A008616.

Sequence in context: A367805 A087822 A163378 * A001319 A240833 A110919

Adjacent sequences: A025807 A025808 A025809 * A025811 A025812 A025813

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved