A159748 If an array is made of columns of -nacci sequences, fibo-, tribo- etc. all starting w. 1,1,2 etc, the NW to SE diagonals can be extended by computation. The above is diagonal 11. See A159741 for details.

144, 927, 2872, 6930, 15109, 31489, 64256, 129792, 260864, 523008, 1047296, 2095872, 4193024, 8387328, 16775936, 33553152, 67107584, 134216448, 268434176, 536869632, 1073740544, 2147482368, 4294966016, 8589933312, 17179867904

Offset: 1

Author

Al Hakanson (hawkuu(AT)gmail.com), Apr 20 2009

Keywords

• nonn

Crossrefs

Cf. A159741 .

Programs

Maple

T := proc(n,m) option remember ; if n < 0 then 0; elif n <= 1 then 1; elif n = 2 then 2; else add(procname(n-i,m),i=1..m) ; fi: end: A159748 := proc(n) T(n+10,n+1) ; end: seq(A159748(n),n=1..40) ; # R. J. Mathar, Apr 22 2009

Formula

a(n) = 3*a(n-1) - 2*a(n-2), n > 8. - R. J. Mathar, Apr 22 2009

Interpolate a(n) = (4*n^5 - 60*n^4 + 415*n^3 - 1665*n^2 + 3826*n + 11745)/15 offset 0 and b(n) = -4*n^5 + 50*n^4 - 305*n^3 + 1127.5*n^2 - 2443.5 + 17430)/15 offset 0. Add the leading 144. Binomially transform. - Al Hakanson (hawkuu(AT)gmail.com), Jun 08 2009

Extensions

More terms from R. J. Mathar, Apr 22 2009