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A082562 a(n) = number of values of m such that m can be expressed as the sum of distinct odd numbers with largest odd number in the sum = 2n+1. 2
1, 2, 4, 8, 15, 24, 35, 48, 63, 80, 99, 120, 143, 168, 195, 224, 255, 288, 323, 360, 399, 440, 483, 528, 575, 624, 675, 728, 783, 840, 899, 960, 1023, 1088, 1155, 1224, 1295, 1368, 1443, 1520, 1599, 1680, 1763, 1848, 1935, 2024, 2115, 2208, 2303, 2400, 2499 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Beginning with the third term, the first differences are the odd positive integers. - John W. Layman, Feb 28 2012

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

For n>2, a(n) = n^2-1. The values of m are all values from 2n+1 to (n+1)^2 except 2n+3 and n^2+2n-1. - David Wasserman, Sep 16 2004

From Colin Barker, Feb 15 2016: (Start)

a(n) = n^2-1 for n>2.

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>5.

G.f.: (1-x+x^2+x^3+x^4-x^5) / (1-x)^3.

(End)

MATHEMATICA

Join[{1, 2, 4}, LinearRecurrence[{3, -3, 1}, {8, 15, 24}, 80]] (* and *) Join[{1, 2, 4}, Table[n^2 - 1, {n, 3, 80}]] (* Vladimir Joseph Stephan Orlovsky, Feb 13 2012 *)

PROG

(PARI) Vec((1-x+x^2+x^3+x^4-x^5)/(1-x)^3 + O(x^100)) \\ Colin Barker, Feb 15 2016

CROSSREFS

Cf. A082548, A082547.

Sequence in context: A026474 A301629 A305992 * A159243 A325840 A324740

Adjacent sequences:  A082559 A082560 A082561 * A082563 A082564 A082565

KEYWORD

easy,nonn

AUTHOR

Naohiro Nomoto, May 05 2003

EXTENSIONS

More terms from David Wasserman, Sep 16 2004

STATUS

approved

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Last modified September 20 03:32 EDT 2019. Contains 327209 sequences. (Running on oeis4.)