OFFSET
0,3
COMMENTS
The length of row n is 4*n+1.
Sum of rows (see example) gives A225828.
This triangle is to A225828 as Losanitsch's triangle A034851 is to A005418, triangle A226048 to A225826, and triangle A226290 to A225827.
Also the number of equivalence classes of ways of placing k 1 X 1 tiles in an n X 4 rectangle under all symmetry operations of the rectangle. - Christopher Hunt Gribble, Apr 24 2015
LINKS
Yosu Yurramendi and María Merino, Rows n = 0..26 of irregular triangle, flattened
EXAMPLE
Irregular triangle:
1
1 2 4 2 1
1 2 10 14 22 14 10 2 1
1 4 22 60 139 208 252 208 139 60 22 4 1
1 4 36 140 476 1092 2044 2860 3270 2860 2044 1092 476 140 36 4 1 ...
MATHEMATICA
T[n_, k_] := (Binomial[4n, k] + If[EvenQ[k], 2 Binomial[2n, k/2], 0] + Sum[Binomial[4 Mod[n, 2], k - 2i] Binomial[4 Quotient[n, 2], i], {i, 0, Quotient[k, 2]}])/4; Table[T[n, k], {n, 0, 5}, {k, 0, 4n}] // Flatten (* Jean-François Alcover, Oct 06 2017, after Andrew Howroyd *)
PROG
(PARI)
T(n, k)={(binomial(4*n, k) + if(k%2==0, 2*binomial(2*n, k/2), 0) + sum(i=0, k\2, binomial(4*(n%2), k-2*i)*binomial(4*(n\2), i)))/4}
for(n=0, 4, for(k=0, 4*n, print1(T(n, k), ", ")); print) \\ Andrew Howroyd, May 30 2017
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Yosu Yurramendi, María Merino, Jul 30 2013
EXTENSIONS
Definition corrected by María Merino, May 19 2017
STATUS
approved