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A157130 Partial sums of A128201. 1
1, 4, 8, 13, 20, 29, 40, 53, 68, 84, 101, 120, 141, 164, 189, 216, 245, 276, 309, 344, 380, 417, 456, 497, 540, 585, 632, 681, 732, 785, 840, 897, 956, 1017, 1080, 1144, 1209, 1276, 1345, 1416, 1489, 1564, 1641, 1720, 1801, 1884, 1969, 2056, 2145, 2236, 2329 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..51.

FORMULA

a(n) = (n-r)^2+(4*r^3+6*r^2+2*r)/3 where r = floor((sqrt(1+8*n)-1)/4). - Simplified by Gerald Hillier, Apr 14 2015

EXAMPLE

First three terms of A128201 are 1, 3, 4, hence a(3) = 1+3+4 = 8.

PROG

(MAGMA) [(n-r)^2+(4*r^3+6*r^2+2*r)/3 where r is Floor((Sqrt(1+8*n)-1)/4): n in [1..51]];

(PARI) {for(n=1, 51, r=floor((sqrt(1+8*n)-1)/4); print1((n-r)^2+(4*r^3+6*r^2+2*r)/3, ", "))}

CROSSREFS

Cf. A128201 (union of A000290 and A005408), A000290 (squares), A005408 (odd numbers).

Sequence in context: A143978 A071994 A023661 * A172050 A312219 A312220

Adjacent sequences:  A157127 A157128 A157129 * A157131 A157132 A157133

KEYWORD

nonn

AUTHOR

Gerald Hillier, Feb 23 2009

EXTENSIONS

Edited and extended by Klaus Brockhaus, Feb 24 2009

STATUS

approved

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Last modified March 20 13:18 EDT 2019. Contains 321345 sequences. (Running on oeis4.)