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 A190717 Triplicated tetrahedral numbers A000292 8
 1, 1, 1, 4, 4, 4, 10, 10, 10, 20, 20, 20, 35, 35, 35, 56, 56, 56, 84, 84, 84, 120, 120, 120, 165, 165, 165, 220, 220, 220, 286, 286, 286, 364, 364, 364, 455, 455, 455, 560, 560, 560, 680, 680, 680, 816, 816, 816, 969, 969, 969 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The Ca1 and Ze3 triangle sums, see A180662 for their definitions, of the triangle A159797 are linear sums of shifted versions of the triplicated tetrahedral numbers, e.g. Ca1(n) = a(n-1) + a(n-2) + 2*a(n-3) + a(n-6). The Ca1, Ca2, Ze3 and Ze4 triangle sums of the Connell sequence A001614 as a triangle are also linear sums of shifted versions of the sequence given above. LINKS Index entries for linear recurrences with constant coefficients, signature (1,0,3,-3,0,-3,3,0,1,-1). FORMULA a(n) = binomial(floor(n/3)+3,3) a(n) + a(n-1) + a(n-2) = A144677(n) a(n) = sum(A144677(n-k)*A049347(k), k=0..n) G.f.: 1/((x-1)^4*(x^2+x+1)^3) MAPLE A190717:= proc(n) option remember; A190717(n):= binomial(floor(n/3)+3, 3) end: seq(A190717(n), n=0..50); MATHEMATICA LinearRecurrence[{1, 0, 3, -3, 0, -3, 3, 0, 1, -1}, {1, 1, 1, 4, 4, 4, 10, 10, 10, 20}, 60] (* Harvey P. Dale, Mar 09 2018 *) CROSSREFS Cf. A000292 (tetrahedral numbers), A058187 (duplicated), A190717 (triplicated), A190718 (quadruplicated). Sequence in context: A219802 A219460 A220010 * A220204 A035618 A220931 Adjacent sequences:  A190714 A190715 A190716 * A190718 A190719 A190720 KEYWORD nonn,easy AUTHOR Johannes W. Meijer, May 18 2011 STATUS approved

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Last modified April 16 00:02 EDT 2021. Contains 343020 sequences. (Running on oeis4.)