A191494 Number of compositions of even natural numbers in 7 parts <= n.

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

Offset: 0

Author

Adi Dani, Jun 03 2011

Keywords

• nonn
• easy

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.

Examples

			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
		

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).

Crossrefs

Cf. A036486 (3 parts), A171714 (4 parts), A191484 (5 parts), A191489 (6 parts), A191495 (8 parts).

Programs

Magma

[((n + 1)^7 + (1+(-1)^n)/2 )/2: n in [0..40]]; // Vincenzo Librandi, Jun 16 2011

Mathematica

Table[1/2*((n + 1)^7 + (1 + (-1)^n)*1/2), {n, 0, 25}]

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