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A218507 Number of partitions of n in which any two parts differ by at most 5. 4
1, 1, 2, 3, 5, 7, 11, 15, 21, 28, 37, 48, 62, 78, 98, 121, 149, 181, 219, 262, 313, 370, 436, 510, 595, 690, 797, 916, 1050, 1198, 1364, 1545, 1747, 1968, 2212, 2479, 2771, 3089, 3437, 3814, 4226, 4669, 5151, 5670, 6232, 6837, 7487, 8185, 8936, 9739, 10602 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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

FORMULA

G.f.: 1 + Sum_{j>0} x^j / Product_{i=0..5} (1-x^(i+j)).

G.f.: (x^20 -x^19 -x^18 +x^15 +x^14 +x^13 -x^12 -x^11 -x^10 +x^7 +x^6 -x^5 +1) / ((x -1)^6*(x +1)^2*(x^2 +1)*(x^2 +x +1)*(x^4 +x^3 +x^2 +x +1)^2). - Colin Barker, Mar 05 2015

MAPLE

b:= proc(n, i, k) option remember; `if`(n<0 or k<0, 0,

      `if`(n=0, 1, `if`(i<1, 0, b(n, i-1, k-1) +b(n-i, i, k))))

    end:

a:= n-> `if`(n=0, 1, 0) +add(b(n-i, i, 5), i=1..n):

seq(a(n), n=0..80);

MATHEMATICA

LinearRecurrence[{1, 1, 0, 0, 0, -2, -2, 1, 1, 2, 1, 1, -2, -2, 0, 0, 0, 1, 1, -1}, {1, 1, 2, 3, 5, 7, 11, 15, 21, 28, 37, 48, 62, 78, 98, 121, 149, 181, 219, 262, 313}, 60] (* Harvey P. Dale, Jan 18 2016 *)

PROG

(PARI) Vec((x^20-x^19-x^18+x^15+x^14+x^13-x^12-x^11-x^10+x^7+x^6-x^5+1)/((x-1)^6*(x+1)^2*(x^2+1)*(x^2+x+1)*(x^4+x^3+x^2+x+1)^2) + O(x^100)) \\ Colin Barker, Mar 05 2015

CROSSREFS

Column k=5 of A194621.

Sequence in context: A049756 A319472 A309099 * A026813 A008636 A008630

Adjacent sequences:  A218504 A218505 A218506 * A218508 A218509 A218510

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Oct 31 2012

STATUS

approved

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Last modified October 1 17:45 EDT 2020. Contains 337444 sequences. (Running on oeis4.)