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A001975 Number of partitions of floor(5n/2) into n nonnegative integers each no more than 5.
(Formerly M2551 N1010)
4
1, 1, 3, 6, 12, 20, 32, 49, 73, 102, 141, 190, 252, 325, 414, 521, 649, 795, 967, 1165, 1394, 1651, 1944, 2275, 2649, 3061, 3523, 4035, 4604, 5225, 5910, 6660, 7483, 8372, 9343, 10395, 11538, 12764, 14090, 15516, 17053, 18691, 20451, 22330, 24342, 26476, 28754 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

In Cayley's terminology, this is the number of literal terms of degree n and of weight floor(5n/2) involving the letters a, b, c, d, e, f, having weights 0, 1, 2, 3, 4, 5 respectively. - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008

REFERENCES

A. Cayley, Numerical tables supplementary to second memoir on quantics, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 2, pp. 276-281.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

A. Cayley, Numerical tables supplementary to second memoir on quantics, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 2, pp. 276-281.

A. Cayley, Numerical tables supplementary to second memoir on quantics, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 2, pp. 276-281. [Annotated scanned copy]

Shalosh B. Ekhad, Doron Zeilberger, In How many ways can I carry a total of n coins in my two pockets, and have the same amount in both pockets?, arXiv:1901.08172 [math.CO], 2019.

FORMULA

Coefficient of x^w*z^n in the expansion of 1/((1-z)(1-xz)(1-x^2z)(1-x^3z)(1-x^4z)(1-x^5z)), where w=floor(5n/2). - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008

G.f.: -(x^14 -x^13 +2*x^12 +x^11 +2*x^10 +3*x^9 +x^8 +5*x^7 +x^6 +3*x^5 +2*x^4 +x^3 +2*x^2 -x+1) / ((x^4+1) *(x^2+x+1) *(x^2-x+1) *(x^2+1)^2 *(x+1)^3 *(x-1)^5). - Alois P. Heinz, Jul 25 2015

PROG

(PARI) f=1/((1-z)*(1-x*z)*(1-x^2*z)*(1-x^3*z)*(1-x^4*z)*(1-x^5*z)); n=350; p=subst(subst(f, x, x+x*O(x^n)), z, z+z*O(z^n)); for(d=0, 60, w=floor(5*d/2); print1(polcoeff(polcoeff(p, w), d)", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008

CROSSREFS

Sequence in context: A066140 A200067 A061061 * A096220 A034333 A182978

Adjacent sequences:  A001972 A001973 A001974 * A001976 A001977 A001978

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Better definition and more terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008

STATUS

approved

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Last modified December 11 12:33 EST 2019. Contains 329916 sequences. (Running on oeis4.)