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A028291 Expansion of 1/((1-x)^2(1-x^2)(1-x^3)(1-x^5)) in powers of x. 1
1, 2, 4, 7, 11, 17, 25, 35, 48, 64, 84, 108, 137, 171, 211, 258, 312, 374, 445, 525, 616, 718, 832, 959, 1100, 1256, 1428, 1617, 1824, 2050, 2297, 2565, 2856, 3171, 3511, 3878, 4273, 4697, 5152, 5639, 6160, 6716, 7309, 7940, 8611, 9324, 10080, 10881, 11729 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Partitions of n into parts 1, 2, 3, and 5. - Joerg Arndt, Jun 05 2014

REFERENCES

Susan Elle, Ore extensions of global dimension 5, Abstract 1110-17-204, Abstracts Amer. Math. Soc., 36 (No. 2, 2015), p. 822.

LINKS

Table of n, a(n) for n=0..48.

Index entries for linear recurrences with constant coefficients, signature (2,0,-1,-1,1,0,-1,1,1,0,-2,1).

FORMULA

a(n) = round((n+1)*(n^3+23*n^2+173*n+451)/720). - Tani Akinari, Jun 05 2014

a(n) - 2*a(n-1) + a(n+3) + a(n+4) - 2*a(n+6) + a(n+7) = 1 if n == 3 (mod 5) else 0. - Michael Somos, Jun 05 2014

a(n) = a(-12 - n) for all n in Z. - Michael Somos, May 14 2015

a(n) - a(n-1) = A008669(n), a(n) - a(n-3) = A001304(n) for all n in Z. - Michael Somos, May 14 2015

Euler transform of length 5 sequence [ 2, 1, 1, 0, 1]. - Michael Somos, May 14 2015

EXAMPLE

G.f. = 1 + 2*x + 4*x^2 + 7*x^3 + 11*x^4 + 17*x^5 + 25*x^6 + 35*x^7 + ...

MATHEMATICA

a[ n_] := Quotient[n (n + 12) (n^2 + 12 n + 52), 720] + 1; (* Michael Somos, Jun 05 2014 *)

a[ n_] := With[{m = If[ n < 0, -12 - n, n]}, SeriesCoefficient[ 1 / ((1 - x)^2*(1 - x^2)*(1 - x^3)*(1 - x^5)), {x, 0, m}]]; (* Michael Somos, Jun 05 2014 *)

Table[Round[(n + 1)*(n^3 + 23*n^2 + 173*n + 451)/720], {n, 0, 40}] (* Wesley Ivan Hurt, Jun 05 2014 *)

PROG

(PARI) Vec(1/((1-x)^2*(1-x^2)*(1-x^3)*(1-x^5))+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

(PARI) {a(n) = n * (n+12) * (n^2 + 12*n + 52) \ 720 + 1}; /* Michael Somos, Jun 05 2014 */

(PARI) {a(n) = if( n<0, n = -12 - n); polcoeff( 1 / ((1 - x)^2 * (1 - x^2) * (1 - x^3) * (1 - x^5)) + x * O(x^n), n)}; /* Michael Somos, Jun 05 2014 */

CROSSREFS

Cf. A001304, A008669.

Sequence in context: A073471 A266901 A117649 * A067997 A175491 A034379

Adjacent sequences:  A028288 A028289 A028290 * A028292 A028293 A028294

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Dec 11 1999

STATUS

approved

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Last modified February 17 02:33 EST 2019. Contains 320200 sequences. (Running on oeis4.)