A270297 Numbers which are representable as a sum of seven but no fewer consecutive nonnegative integers.

28, 56, 112, 196, 224, 308, 364, 392, 448, 476, 532, 616, 644, 728, 784, 812, 868, 896, 952, 1036, 1064, 1148, 1204, 1232, 1288, 1316, 1372, 1456, 1484, 1568, 1624, 1652, 1708, 1736, 1792, 1876, 1904, 1988, 2044, 2072, 2128, 2156, 2212, 2296, 2324, 2408, 2464

Offset

1,1

Links

Ray Chandler, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,1,-1).

Formula

A163169(a(n)) = 7. - Ray Chandler, Mar 22 2016

a(n) = 28*A229829(n). - Hugo Pfoertner, Feb 04 2021

G.f.: 28*x*(1 +x +2*x^2 +3*x^3 +x^4 +3*x^5 +2*x^6 +x^7 +x^8) / ((1-x)^2*(1+x)*(1+x^2)*(1+x^4)). - Andrew Howroyd, Oct 31 2025

Example

28 = 1 + 2 + 3 + 4 + 5 + 6 + 7;
35 = 2 + 3 + 4 + 5 + 6 + 7 + 8 = 17 + 18 (not in sequence);
56 = 5 + 6 + 7 + 8 + 9 + 10 + 11;
112 = 13 + 14 + 15 + 16 + 17 + 18 + 19.

Prog

(PARI) a(n)=28+((n-1)\8)*420+[364, 0, 28, 84, 168, 196, 280, 336][n%8+1] \\ Charles R Greathouse IV, May 13 2026

Crossrefs

Cf. A138591, A229829, A270296, A270298, A270299, A270300, A270301, A270302, A270303.

Sequence in context: A135628 A204646 A211491 * A068576 A272185 A093290

Adjacent sequences: A270294 A270295 A270296 * A270298 A270299 A270300

Keyword

nonn,easy

Author

Martin Renner, Mar 14 2016

Status

approved