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A101338 Antidiagonal sums in A101321. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A175104

Adjacent sequences:  A101335 A101336 A101337 * A101339 A101340 A101341

KEYWORD

nonn,easy,changed

AUTHOR

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

STATUS

approved

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Last modified January 20 02:13 EST 2019. Contains 319320 sequences. (Running on oeis4.)