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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

Adi Dani, Restricted compositions of natural numbers

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 June 22 17:19 EDT 2018. Contains 305672 sequences. (Running on oeis4.)