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A025810 Expansion of 1/((1-x^2)(1-x^5)(1-x^10)) in powers of x. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A135023 A087822 A163378 * A001319 A240833 A110919

Adjacent sequences:  A025807 A025808 A025809 * A025811 A025812 A025813

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified August 7 15:30 EDT 2020. Contains 336276 sequences. (Running on oeis4.)