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

1,1

Links

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

Example

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

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 *)

Crossrefs

Cf. A002522.

Sequence in context: A341122 A237825 A194939 * A238007 A204207 A354704

Adjacent sequences: A135632 A135633 A135634 * A135636 A135637 A135638

Keyword

nonn,tabl

Author

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

Extensions

More terms from Emeric Deutsch, Mar 03 2008

Status

approved