A101338 Antidiagonal sums in A101321.

1, 2, 4, 9, 20, 41, 77, 134, 219, 340, 506, 727, 1014, 1379, 1835, 2396, 3077, 3894, 4864, 6005, 7336, 8877, 10649, 12674, 14975, 17576, 20502, 23779, 27434, 31495, 35991, 40952, 46409, 52394, 58940, 66081, 73852, 82289, 91429, 101310, 111971

Offset: 0

Author

Eugene McDonnell (eemcd(AT)mac.com), Dec 24 2004

Keywords

• nonn
• easy

Comments

Equals binomial transform of [1, 1, 1, 2, 1, 0, 0, 0, ...]. Example: a(5) = 20 = [1, 1, 1, 2, 1] dot [1, 4, 6, 4, 1] = (1 + 4 + 6 + 8 + 1). - Gary W. Adamson, Aug 25 2010

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Crossrefs

Cf. A000127, A000292.

Programs

Mathematica

CoefficientList[Series[(1-3*x+4*x^2-x^3)/(1-x)^5,{x,0,40}],x] (* Vincenzo Librandi, Mar 24 2012 *)
LinearRecurrence[{5,-10,10,-5,1},{1,2,4,9,20},50] (* Harvey P. Dale, May 21 2013 *)

Formula

a(n) = n^4/24 + n^3/12 - n^2/24 + 11*n/12 + 1.

G.f.: (1-3*x+4*x^2-x^3)/(1-x)^5. - Colin Barker, Mar 22 2012

a(0)=1, a(1)=2, a(2)=4, a(3)=9, a(4)=20, a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Harvey P. Dale, May 21 2013

a(n) = A000127(n+1) + A000292(n-2). - Bruce J. Nicholson, Jan 06 2019