A274627 Product_{i=0..3} (2^floor((n+i)/4)-1).

0, 0, 0, 0, 1, 3, 9, 27, 81, 189, 441, 1029, 2401, 5145, 11025, 23625, 50625, 104625, 216225, 446865, 923521, 1876833, 3814209, 7751457, 15752961, 31755969, 64016001, 129048129, 260144641, 522337665, 1048788225, 2105834625, 4228250625, 8473082625, 16979393025, 34025371905, 68184176641

Offset: 0

Author

N. J. A. Sloane, Jul 05 2016

Keywords

• nonn

Comments

This is a four-dimensional analog of the holes-in-sheet-of-paper sequence A274230. See A274230 and A274626 for further information.

References

• Tom Karzes, Posting to Math Fun Mailing List, Jul 05 2016.

Crossrefs

Cf. A274230, A274626.

Programs

Maple

f:=(n,d) -> mul(2^floor((n+i)/d)-1, i = 0 .. d-1);
[seq(f(n,4),n=0..40)];

PARI

a(n) = prod(i=0, 3, 2^floor((n+i)/4)-1) \\ Colin Barker, Jul 06 2016

Formula

Empirical g.f.: x^4*(1+2*x^2+6*x^3+4*x^4+8*x^6) / ((1-x)*(1-2*x)*(1-2*x^2)*(1+2*x^2)*(1-2*x^4)*(1-8*x^4)). - Colin Barker, Jul 06 2016