A093039 Sequence resulting from a sum of three repeated binomial(n+3,4) sequences.

1, 2, 7, 11, 25, 35, 65, 85, 140, 175, 266, 322, 462, 546, 750, 870, 1155, 1320, 1705, 1925, 2431, 2717, 3367, 3731, 4550, 5005, 6020, 6580, 7820, 8500, 9996, 10812, 12597, 13566, 15675, 16815, 19285, 20615, 23485, 25025, 28336, 30107, 33902

Offset: 1

Author

Alford Arnold, May 08 2004

Keywords

• nonn
• easy

Comments

Euler transform of length 3 sequence [2,k,-1] with k=4 (cf. A028724 for k=3). - Georg Fischer, Nov 28 2020

Examples

			b(n) = 1,  1,  5,  5, 15, 15, 35, 35, 70, 70,126,126
     + 0,  1,  1,  5,  5, 15, 15, 35, 35, 70, 70,126
     + 0,  0,  1,  1,  5,  5, 15, 15, 35, 35, 70, 70
     -----------------------------------------------
a(n) = 1,  2,  7, 11, 25, 35, 65, 85,140,175,266,322
		

Crossrefs

Cf. A001651(k=1), A001318(k=2), A028724(k=3).

Cf. repeated binomial coefficients: A008805(k=2), A058187(k=3), A189976(k=4).

Programs

Mathematica

k := 4; nmax := 32; a := Flatten[Table[{Binomial[n,k], Binomial[n,k]},{n,k,nmax}]];
a + Flatten[Join[{0}, Drop[a,-1]]] + Flatten[Join[{0,0}, Drop[a,-2]]] (* Georg Fischer, Nov 29 2020 *)

Formula

a(1) = b(1), a(2) = b(2), a(n) = b(n) + b(n-1) + b(n-2) for n > 2, where k = 4 and b(n) = binomial(floor((n+7)/2), k) = A189976(n-7).

Extensions

More terms from and edited by Georg Fischer, Nov 28 2020