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 A189374 Expansion of 1/((1-x)^5*(x^2+x+1)^3). 4
 1, 2, 3, 7, 11, 15, 25, 35, 45, 65, 85, 105, 140, 175, 210, 266, 322, 378, 462, 546, 630, 750, 870, 990, 1155, 1320, 1485, 1705, 1925, 2145, 2431, 2717, 3003, 3367, 3731, 4095, 4550, 5005, 5460, 6020, 6580, 7140, 7820 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The Ca1(n) and Ze3(n) triangle sums of A139600 lead to the sequence given above, see the formulas. For the definitions of these triangle sums see A180662. LINKS Index entries for linear recurrences with constant coefficients, signature (2,-1,3,-6,3,-3,6,-3,1,-2,1) FORMULA a(n) = (2*a(n-1) + 2*a(n-2) + (8+n)*a(n-3))/n with a(0)=1, a(1)=2, a(2)=3 and a(3)=7. a(n) = sum(A011779(n-k)*A049347(k), k=0..n). Ca1(n) = A189374(n-3) - A189374(n-4) - A189374(n-6) + 2*A189374(n-7). Ze3(n) = 2*A189374(n-3) - A189374(n-4) - 2*A189374(n-6) + 5*A189374(n-7) with A189374(n)=0 for n <= -1. a(n) = (floor(n/3)+1)*(floor(n/3)+2)*(floor(n/3)+3)*(3*floor(n/3)+4*(4-(3*floor((n+3)/3)-n)))/24. - Luce ETIENNE, Jun 29 2015 MAPLE a:= proc(n) option remember; `if` (n<4, [1, 2, 3, 7][n+1], (2*a(n-1) +2*a(n-2) +(8+n) *a(n-3))/n) end: seq (a(n), n=0..50); CROSSREFS Cf. A139600, A189375, A189376. Sequence in context: A174060 A285278 A092353 * A180516 A100963 A342029 Adjacent sequences:  A189371 A189372 A189373 * A189375 A189376 A189377 KEYWORD easy,nonn AUTHOR Johannes W. Meijer, Apr 29 2011 STATUS approved

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Last modified December 3 22:32 EST 2021. Contains 349468 sequences. (Running on oeis4.)