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 A160538 a(n) = 4*(n^4-n^3). 0
 0, 32, 216, 768, 2000, 4320, 8232, 14336, 23328, 36000, 53240, 76032, 105456, 142688, 189000, 245760, 314432, 396576, 493848, 608000, 740880, 894432, 1070696, 1271808, 1500000, 1757600, 2047032, 2370816, 2731568, 3132000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is the number of edges in a four-dimensional hypercube (a tesseract) having sides of length n. LINKS Table of n, a(n) for n=1..30. Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA O.g.f.: (32*x^2+56*x^3+8*x^4)/(1-x)^5. E.g.f.: 4*exp(x)*x^2 (4 + 5 x + x^2). From Amiram Eldar, Jan 14 2021: (Start) Sum_{n>=2} 1/a(n) = 3/4 - Pi^2/24 - zeta(3)/4. Sum_{n>=2} (-1)^n/a(n) = -3/4 + Pi^2/48 + log(2)/2 + 3*zeta(3)/16. (End) EXAMPLE a(1) = 32 because the four dimensional unit hypercube has 32 edges. MATHEMATICA Table[4 (n^4 - n^3), {n, 20}] LinearRecurrence[{5, -10, 10, -5, 1}, {0, 32, 216, 768, 2000}, 30] (* Harvey P. Dale, Nov 05 2017 *) PROG (PARI) a(n)=4*(n^4-n^3) \\ Charles R Greathouse IV, Oct 21 2022 CROSSREFS Cf. A046092, A059986. Sequence in context: A119286 A125342 A126500 * A200787 A250354 A146089 Adjacent sequences: A160535 A160536 A160537 * A160539 A160540 A160541 KEYWORD nonn,easy AUTHOR Geoffrey Critzer, May 18 2009 EXTENSIONS More terms from Harvey P. Dale, Nov 05 2017 Offset corrected by Amiram Eldar, Jan 14 2021 STATUS approved

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Last modified September 25 11:00 EDT 2023. Contains 365644 sequences. (Running on oeis4.)