A176226 A symmetrical triangle sequence: T(n, k) = q^k + q^(n-k) - q^n, with q=5.

1, 1, 1, 1, -15, 1, 1, -95, -95, 1, 1, -495, -575, -495, 1, 1, -2495, -2975, -2975, -2495, 1, 1, -12495, -14975, -15375, -14975, -12495, 1, 1, -62495, -74975, -77375, -77375, -74975, -62495, 1, 1, -312495, -374975, -387375, -389375, -387375, -374975, -312495, 1

Offset

0,5

Comments

Row sums are: {1, 2, -13, -188, -1563, -10938, -70313, -429688, -2539063, -14648438, -83007813, ...}.

Links

G. C. Greubel, Rows n = 0..100 of triangle, flattened

Formula

T(n,k) = q^k + q^(n-k) - q^n, with q = 5.

Example

Triangle begins as:
  1;
  1,      1;
  1,    -15,      1;
  1,    -95,    -95,      1;
  1,   -495,   -575,   -495,      1;
  1,  -2495,  -2975,  -2975,  -2495,      1;
  1, -12495, -14975, -15375, -14975, -12495,      1;   1, -62495, -74975, -77375, -77375, -74975, -62495, 1;

Maple

q:=5; seq(seq(q^k +q^(n-k) -q^n, k=0..n), n=0..12); # G. C. Greubel, Nov 23 2019

Mathematica

T[n_, k_, q_]:= q^k +q^(n-k) -q^n; Table[T[n, k, 5], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Nov 23 2019 *)

Prog

(PARI) T(n, k, q) = my(q=5); q^k +q^(n-k) -q^n; \\ G. C. Greubel, Nov 23 2019
(Magma) q:=5; [q^k +q^(n-k) -q^n : k in [0..n], n in [0..12]]; // G. C. Greubel, Nov 23 2019
(Sage) q=5; [[q^k +q^(n-k) -q^n for k in (0..n)] for n in (0..12)] # G. C. Greubel, Nov 23 2019
(GAP) q:=5;; Flat(List([0..12], n-> List([0..n], k-> q^k +q^(n-k) -q^n ))); # G. C. Greubel, Nov 23 2019

Crossrefs

Cf. A176224 (q=2), A176225 (q=3), this sequence (q=5), A176227 (q=4).

Sequence in context: A176286 A111805 A238754 * A155493 A156939 A174187

Adjacent sequences: A176223 A176224 A176225 * A176227 A176228 A176229

Keyword

sign,tabl

Author

Roger L. Bagula, Apr 12 2010

Extensions

Edited by G. C. Greubel, Nov 23 2019

Status

approved