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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

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).

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);

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 May 23 16:47 EDT 2017. Contains 286925 sequences.