A135635 Triangle read by rows, constructed by the Pascal rule, with top entry 2, left edge = odd numbers, right edge = squares plus 1.

2, 3, 5, 5, 8, 10, 7, 13, 18, 17, 9, 20, 31, 35, 26, 11, 29, 51, 66, 61, 37, 13, 40, 80, 117, 127, 98, 50, 15, 53, 120, 197, 244, 225, 148, 65, 17, 68, 173, 317, 441, 469, 373, 213, 82, 19, 85, 241, 490, 758, 910, 842, 586, 295, 101

Offset: 1

Author

David Williams (davidwilliams(AT)paxway.com), Mar 01 2008

Keywords

• nonn
• tabl

Examples

			............2
...........3.5
..........5.8.10
........7.13.18.17
.......9.20.31.35.26
.....11.29.51.66.61.37
		

Links

• G. C. Greubel, Table of n, a(n) for the first 25 rows

Crossrefs

Cf. A002522.

Programs

Maple

T:=proc(n,k)if n=1 and k=1 then 2 elif k=1 then 2*n-1 elif n < k then 0 elif k =n then n^2+1 else T(n-1,k)+T(n-1,k-1) end if end proc: for n to 10 do seq(T(n,k),k=1..n) end do; # yields sequence in triangular form - Emeric Deutsch, Mar 03 2008

Mathematica

T[1, 1]:= 2; T[n_, 1]:= 2*n - 1; T[n_, n_]:= n^2 + 1; T[n_, k_] := T[n - 1, k] + T[n - 1, k - 1]; Table[T[n, k], {n, 1, 10}, {k, 1, n}]//Flatten (* G. C. Greubel, Oct 25 2016 *)

Extensions

More terms from Emeric Deutsch, Mar 03 2008