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A130404 Partial sums of A093178. 1
1, 2, 3, 6, 7, 12, 13, 20, 21, 30, 31, 42, 43, 56, 57, 72, 73, 90, 91, 110, 111, 132, 133, 156, 157, 182, 183, 210, 211, 240, 241, 272, 273, 306, 307, 342, 343, 380, 381, 420, 421, 462, 463, 506, 507, 552, 553, 600, 601, 650, 651, 702, 703, 756, 757, 812, 813 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers n such that floor(n/2) is a positive triangular number. - Bruno Berselli, Sep 15 2014

LINKS

Table of n, a(n) for n=1..57.

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

FORMULA

a(1) = 1; for n > 1, a(n) = a(n-1)+1 if n is odd, a(n) = a(n-1)+(n-1) if n is even.

a(n) = A002061((n+1)/2) = (n^2+3)/4 if n is odd, a(n) = A002378(n/2) = (n^2+2*n)/4) if n is even.

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

a(n) = A093178(n) - A093178(n-1).

a(1) = 1; a(n) = a(n-1) + n^(n mod 2) = (1/4)*(n^2 + 2n + 4 + (n mod 2)*(2n-1)). - Rolf Pleisch, Feb 04 2008

a(n) = (2*(n-1)*(n+2) + (2*n-3)*(-1)^n+7)/8. - Bruno Berselli, Mar 31 2011

MATHEMATICA

Table[If[EvenQ[n], 1, n], {n, 0, 56}] // Accumulate (* Jean-Fran├žois Alcover, Jun 10 2013 *)

Accumulate[Join[{1}, Riffle[Range[1, 85, 2], 1]]] (* or *) LinearRecurrence[ {1, 2, -2, -1, 1}, {1, 2, 3, 6, 7}, 90] (* Harvey P. Dale, Jun 01 2016 *)

PROG

(PARI) {s=0; for(n=1, 57, s=s+if(n%2>0, 1, n-1); print1(s, ", "))}

(PARI) {for(n=1, 57, print1(if(n%2>0, (n^2+3)/4, (n^2+2*n)/4), ", "))}

(MAGMA) &cat[ [ n^2-n+1, n*(n+1) ]: n in [1..29] ];

CROSSREFS

Cf. A093178, A002061, A002378, A247375.

Sequence in context: A101319 A182538 A030013 * A064689 A240175 A238590

Adjacent sequences:  A130401 A130402 A130403 * A130405 A130406 A130407

KEYWORD

nonn,easy

AUTHOR

Klaus Brockhaus, May 25 2007

STATUS

approved

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Last modified November 17 23:26 EST 2019. Contains 329242 sequences. (Running on oeis4.)