A350498 - OEIS

A350498

Convolution of triangular numbers with every third number of Narayana's Cows sequence.

0, 1, 7, 31, 114, 385, 1250, 3987, 12619, 39810, 125425, 394955, 1243433, 3914383, 12322293, 38789576, 122105944, 384377494, 1209981891, 3808901216, 11990036895, 37743426054, 118812495000, 374009739009, 1177344897390, 3706162867858, 11666626518622, 36725362368682, 115607732787126, 363921470561515

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OFFSET

1,3

COMMENTS

This is the convolution of N(3*n-1) with t(n); in other words, a(n) = Sum_{i=1..n} N(3*i-1)*t(n-i) where N(k)=A000930(k) is the k-th number in Narayana's Cows sequence and t(k)=A000217(k) is the k-th triangular number.

REFERENCES

G. Dresden and M. Tulskikh, "Convolutions of Sequences with Single-Term Signature Differences", preprint.

LINKS

Table of n, a(n) for n=1..30.

Index entries for linear recurrences with constant coefficients, signature (7,-18,23,-16,6,-1).

FORMULA

a(n) = N(3*n-1) - A000217(n) where N(k)=A000930(k).

G.f.: x^2/((1 - x)^3 * (1 - 4*x + 3*x^2 - x^3)).

a(n) = A052529(n)-A000217(n), n>0. - R. J. Mathar, Aug 17 2022

EXAMPLE

For n=4, a(4) = N(2)*t(3) + N(5)*t(2) + N(8)*t(1) + N(11)*t(0) = 1*6 + 4*3 + 13*1 + 41*0 = 31, where N(k)=A000930(k) and t(k)=A000217(k).

MATHEMATICA