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 A091498 The sixth column of triangle A091492, excluding leading zeros. 1
 1, 2, 3, 5, 8, 11, 17, 23, 31, 41, 54, 68, 88, 109, 135, 165, 202, 241, 291, 344, 407, 477, 559, 646, 751, 862, 990, 1129, 1288, 1456, 1651, 1857, 2089, 2338, 2617, 2911, 3244, 3594, 3982, 4395, 4851, 5330, 5862, 6420, 7031, 7677, 8382, 9120, 9929, 10775 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Excluding leading zeros, columns k=3,4,5, of triangle A091492 list the partitions of n into k parts. This sequence is related to the partitions of n into at most 6 parts (A001402) since A(x)=(1+x-x^5)*G001402(x), where G001402(x) is the g.f. for A001402. LINKS Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 0, -1, 0, -2, 0, 1, 1, 1, 1, 0, -2, 0, -1, 0, 0, 1, 1, -1). FORMULA G.f.: (1+x-x^5)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)) a(0)=1, a(1)=2, a(2)=3, a(3)=5, a(4)=8, a(5)=11, a(6)=17, a(7)=23, a(8)=31, a(9)=41, a(10)=54, a(11)=68, a(12)=88, a(13)=109, a(14)=135, a(15)=165, a(16)=202, a(17)=241, a(18)=291, a(19)=344, a(20)=407, a(n)=a(n-1)+ a(n-2)- a(n-5)-2*a(n-7)+a(n-9)+a(n-10)+a(n-11)+a(n-12)-2*a(n-14)-a(n-16)+ a(n-19)+ a(n-20)-a (n-21). - Harvey P. Dale, Dec 09 2012 MATHEMATICA CoefficientList[Series[(1+x-x^5)/((1-x)(1-x^2)(1-x^3)(1-x^4)(1-x^5)(1-x^6)), {x, 0, 60}], x] (* or *) LinearRecurrence[ {1, 1, 0, 0, -1, 0, -2, 0, 1, 1, 1, 1, 0, -2, 0, -1, 0, 0, 1, 1, -1}, {1, 2, 3, 5, 8, 11, 17, 23, 31, 41, 54, 68, 88, 109, 135, 165, 202, 241, 291, 344, 407}, 60](* Harvey P. Dale, Dec 09 2012 *) PROG (PARI) {a(n)=polcoeff( (1+x-x^5)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)) +O(x^(n+1)), n, x)} CROSSREFS Cf. A091492, A091493, A001402. Sequence in context: A046938 A060677 A131787 * A227562 A000511 A263710 Adjacent sequences:  A091495 A091496 A091497 * A091499 A091500 A091501 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 16 2004 STATUS approved

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Last modified June 17 22:17 EDT 2019. Contains 324200 sequences. (Running on oeis4.)