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A055268 a(n) = (11*n+4)*C(n+3, 3)/4. 3
1, 15, 65, 185, 420, 826, 1470, 2430, 3795, 5665, 8151, 11375, 15470, 20580, 26860, 34476, 43605, 54435, 67165, 82005, 99176, 118910, 141450, 167050, 195975, 228501, 264915, 305515, 350610, 400520, 455576, 516120, 582505, 655095, 734265 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is the number of compositions of n when there are 9 types of each natural number. - Milan Janjic, Aug 13 2010

Convolution of A000027 with A051865 (excluding 0). - Bruno Berselli, Dec 07 2012

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 122-125, 194-196.

LINKS

Table of n, a(n) for n=0..34.

I. Adler, Three Diophantine equations - Part II, Fib. Quart., 7 (1969), pp. 181-193.

E. I. Emerson, Recurrent Sequences in the Equation DQ^2=R^2+N, Fib. Quart., 7 (1969), pp. 231-242.

Index to sequences related to pyramidal numbers

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

G.f.: (-1-10*x) / (x-1)^5. - R. J. Mathar, Oct 26 2011

PROG

(MAGMA) /* A000027 convolved with A051865 (excluding 0): */ A051865:=func<n | n*(11*n-9)/2>; [&+[(n-i+1)*A051865(i): i in [1..n]]: n in [1..35]]; // Bruno Berselli, Dec 07 2012

(Python)

A055268_list, m = [], [11, 1, 1, 1, 1]

for _ in range(10**2):

    A055268_list.append(m[-1])

    for i in range(4):

        m[i+1] += m[i] # Chai Wah Wu, Jan 24 2016

(PARI) a(n) = (11*n+4)*binomial(n+3, 3)/4; \\ Michel Marcus, Sep 07 2017

CROSSREFS

Partial sums of A050441.

Cf. A000292, A051865.

Cf. A220212 for a list of sequences produced by the convolution of the natural numbers with the k-gonal numbers.

Sequence in context: A218216 A027455 A152729 * A090026 A027526 A284898

Adjacent sequences:  A055265 A055266 A055267 * A055269 A055270 A055271

KEYWORD

nonn,easy

AUTHOR

Barry E. Williams, May 10 2000

STATUS

approved

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Last modified October 14 09:57 EDT 2019. Contains 327995 sequences. (Running on oeis4.)