

A114214


Diagonal sums of number triangle A114213.


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


LINKS

Table of n, a(n) for n=0..84.
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..n2k} C(k, j) C(n2k, 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, n2*k, binomial(k, j)*binomial(n2*k, j)*(1+(1)^j)/2) % 2); \\ Michel Marcus, Jun 06 2021


CROSSREFS

Cf. 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



