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 A191494 Number of compositions of even natural numbers in 7 parts <= n. 3
 1, 64, 1094, 8192, 39063, 139968, 411772, 1048576, 2391485, 5000000, 9743586, 17915904, 31374259, 52706752, 85429688, 134217728, 205169337, 306110016, 446935870, 640000000, 900544271, 1247178944, 1702412724, 2293235712, 3051757813, 4015905088 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Number of ways of placing an even number of indistinguishable objects in 7 distinguishable boxes with the condition that in each box can be at most n objects. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (7,-20,28,-14,-14,28,-20,7,-1). FORMULA a(n) = ((n + 1)^7 + (1 + (-1)^n)/2 )/2. G.f.: ( 1 + 57*x + 666*x^2 + 1786*x^3 + 1821*x^4 + 645*x^5 + 64*x^6 ) / ( (1+x)*(x-1)^8 ). - R. J. Mathar, Jun 08 2011 EXAMPLE a(1)=64 and compositions of even natural numbers into 7 parts no greater than 1 are :(0,0,0,0,0,0,0) --> 7!/7!0! = 1 :(0,0,0,0,0,1,1) --> 7!/5!2! = 21 :(0,0,0,1,1,1,1) --> 7!/3!4! = 35 :(0,1,1,1,1,1,1) --> 7!/1!6! = 7 MATHEMATICA Table[1/2*((n + 1)^7 + (1 + (-1)^n)*1/2), {n, 0, 25}] PROG (Magma) [((n + 1)^7 + (1+(-1)^n)/2 )/2: n in [0..40]]; // Vincenzo Librandi, Jun 16 2011 CROSSREFS Cf. A036486 (3 parts), A171714 (4 parts), A191484 (5 parts), A191489 (6 parts), A191495 (8 parts). Sequence in context: A301490 A223070 A191900 * A269000 A189276 A081102 Adjacent sequences: A191491 A191492 A191493 * A191495 A191496 A191497 KEYWORD nonn,easy AUTHOR Adi Dani, Jun 03 2011 STATUS approved

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Last modified February 7 05:08 EST 2023. Contains 360112 sequences. (Running on oeis4.)