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A101427 Number of different cuboids with volume (pq)^n, where p,q are distinct prime numbers. 6
1, 2, 8, 19, 42, 78, 139, 224, 350, 517, 744, 1032, 1405, 1862, 2432, 3115, 3942, 4914, 6067, 7400, 8954, 10729, 12768, 15072, 17689, 20618, 23912, 27571, 31650, 36150, 41131, 46592, 52598, 59149, 66312, 74088, 82549, 91694, 101600, 112267, 123774 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Subsequence of A034836, which gives the number of cuboids for volume n.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (2,1,-3,-1,1,3,-1,-2,1)

FORMULA

If n is a multiple of 3, a(n) = ((n+2)^2*(n+1)^2 + 12*(floor(n/2)+1)^2+8)/24, otherwise a(n) = ((n+2)^2*(n+1)^2 + 12*(floor(n/2)+1)^2)/24. - Frederic Solbes, Mar 18 2014

G.f.: -(x^6+3*x^4+4*x^3+3*x^2+1)/((x^2+x+1)*(x+1)^2*(x-1)^5). - Colin Barker, Mar 27 2014

From Daniel Mondot, Sep 20 2016: (Start)

a(n) = a(n-1) + 2*a(n-2) - a(n-3) - 2*a(n-4) - a(n-5) + 2*a(n-6) + a(n-7) - a(n-8) + 12, n>=8.

a(n) = 4*a(n-6) - 6*a(n-12) + 4*a(n-18) - a(n-24) + 1296, n>=24. (End)

MATHEMATICA

a[n_] := Switch[Mod[n, 6], 0, n+1, 1|5, 3n/4 + 7/24, 2|4, n+2/3, 3, 3n/4 + 5/8] + n^4/24 + n^3/4 + 2n^2/3; Table[a[n], {n, 0, 40}] (* Jean-Fran├žois Alcover, Oct 06 2016, after Frederic Solbes' formula *)

PROG

(PARI) a(n) = if (n % 3, ((n+2)^2*(n+1)^2 + 12*(n\2+1)^2)/24, ((n+2)^2*(n+1)^2 + 12*(n\2+1)^2+8)/24); \\ Michel Marcus, Mar 18 2014

CROSSREFS

Cf. A034836, A101423, A101424, A101425, A101426.

Column k=3 of A277239.

Sequence in context: A240279 A327728 A000158 * A286269 A126877 A107769

Adjacent sequences:  A101424 A101425 A101426 * A101428 A101429 A101430

KEYWORD

nonn

AUTHOR

Anthony C Robin, Jan 17 2005

EXTENSIONS

Extended by Ray Chandler, Dec 17 2008

Edited by Ray Chandler, Dec 19 2008

a(0) = 1 prepended by Daniel Mondot, Sep 20 2016

STATUS

approved

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Last modified January 20 11:11 EST 2020. Contains 331083 sequences. (Running on oeis4.)