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A190717
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Triplicated tetrahedral numbers A000292
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8
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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
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OFFSET
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0,4
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=0..50.
Index entries for linear recurrences with constant coefficients, signature (1,0,3,-3,0,-3,3,0,1,-1).
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FORMULA
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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)
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MAPLE
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A190717:= proc(n) option remember; A190717(n):= binomial(floor(n/3)+3, 3) end: seq(A190717(n), n=0..50);
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MATHEMATICA
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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 *)
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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Johannes W. Meijer, May 18 2011
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STATUS
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approved
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