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

0,2

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).

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

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 *)

Crossrefs

Cf. A000127, A000292.

Sequence in context: A053024 A240047 A090166 * A018102 A018103 A350092

Adjacent sequences: A101335 A101336 A101337 * A101339 A101340 A101341

Keyword

nonn,easy

Author

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

Status

approved