a(n,m) tabl head (triangle) for A128495 = S(2;n,m) Coefficient triangle of sums of squares of Chebyshev's S-polynomials. n\m 0 1 2 3 4 5 6 7 8 9 10... 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 2 2 -1 1 0 0 0 0 0 0 0 0 3 2 3 -3 1 0 0 0 0 0 0 0 4 3 -3 8 -5 1 0 0 0 0 0 0 5 3 6 -16 17 -7 1 0 0 0 0 0 6 4 -6 30 -45 30 -9 1 0 0 0 0 7 4 10 -50 103 -98 47 -11 1 0 0 0 8 5 -10 80 -211 269 -183 68 -13 1 0 0 9 5 15 -120 399 -651 588 -308 93 -15 1 0 10 6 -15 175 -707 1432 -1644 1136 -481 122 -17 1 . . . The rows n=11..15 are: n=11: [6, 21, -245, 1190, -2920, 4132, -3608, 2005, -710, 155, -19, 1] n=12: [7, -21, 336, -1918, 5598, -9540, 10212, -7137, 3303, -1003, 192, -21, 1] n=13: [7, 28, -448, 2982, -10194, 20546, -26356, 22481, -13033, 5154, -1368, 233, -23, 1] n=14: [8, -28, 588, -4494, 17772, -41746, 63046, -64181, 45244, -22338, 7698, -1813, 278, -25, 1] n=15: [8, 36, -756, 6594, -29844, 80718, -141482, 168927, -141636, 84766, -36366, 11091, -2346, 327, -27, 1] ############################################################################################################# Row sums (signed)look like A004523: [1,2,2,3,4,4,5,6,6,7,8,8,9,10,10,11, ...], with g.f. (1+2*x+2*x^2+x^3)/(1-x^3)^2 (Len Smiley). Row sums (unsigned) A128495: [1,2,4,9,20,50,125,324,840,2195,5736,15012,39289,102854,269260,704925,..] ###################################### e.o.f.################################################################