A114214 Diagonal sums of number triangle A114213.

1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 4, 4, 5, 5, 7, 7, 8, 8, 7, 7, 7, 7, 8, 8, 7, 7, 5, 5, 6, 6, 9, 9, 11, 11, 10, 10, 11, 11, 13, 13, 12, 12, 9, 9, 9, 9, 12, 12, 13, 13, 11, 11, 10, 10, 11, 11, 9, 9, 6, 6, 7, 7, 11, 11, 14, 14, 13, 13, 15, 15, 18, 18, 17, 17, 13, 13, 14, 14, 19, 19, 21

Offset

0,3

Comments

Conjecture: a(n) = A007306(floor(n/2)+1). - Georg Fischer, Nov 28 2022

Links

Georg Fischer, Table of n, a(n) for n = 0..1000

Jeffrey Shallit and Lukas Spiegelhofer, Continuants, run lengths, and Barry's modified Pascal triangle, arXiv:1710.06203 [math.CO], 2017.

Formula

a(n) = Sum_{k=0..floor(n/2)} mod(Sum_{j=0..n-2k} C(k, j) C(n-2k, j) (1+(-1)^j)/2, 2). (corrected by Jeffrey Shallit, May 18 2016)

Prog

(PARI) a(n) = sum(k=0, n\2, sum(j=0, n-2*k, binomial(k, j)*binomial(n-2*k, j)*(1+(-1)^j)/2) % 2); \\ Michel Marcus, Jun 06 2021

Crossrefs

Cf. A007306, A114213.

Sequence in context: A093875 A329242 A266193 * A321318 A270362 A196383

Adjacent sequences: A114211 A114212 A114213 * A114215 A114216 A114217

Keyword

easy,nonn

Author

Paul Barry, Nov 17 2005

Status

approved