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A167487 a(n) = n*(n + 3)/2 + 8. 3
8, 10, 13, 17, 22, 28, 35, 43, 52, 62, 73, 85, 98, 112, 127, 143, 160, 178, 197, 217, 238, 260, 283, 307, 332, 358, 385, 413, 442, 472, 503, 535, 568, 602, 637, 673, 710, 748, 787, 827, 868, 910, 953, 997, 1042, 1088, 1135, 1183, 1232, 1282, 1333, 1385, 1438 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

2*a(i) + 3 is prime for i = 0..14. - Vincenzo Librandi, Jun 01 2014

Numbers m >= 8 such that 8*m-55 is a square. - Bruce J. Nicholson, Jul 26 2017

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = n + a(n-1) + 1 with n>1, a(1)=10.

G.f.: (8 - 14*x + 7*x^2)/(1 - x)^3. - Vincenzo Librandi, Sep 16 2013

a(n) = Sum_{i=n-5..n+7} i*(i+1)/26. - Bruno Berselli, Oct 20 2016

MATHEMATICA

Table[n (n + 3)/2 + 8, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 03 2011 *)

CoefficientList[Series[(8 - 14 x + 7 x^2) / (1 - x)^3, {x, 0, 60}], x] (* Vincenzo Librandi, Sep 16 2013 *)

LinearRecurrence[{3, -3, 1}, {8, 10, 13}, 60] (* Harvey P. Dale, Jul 05 2020 *)

PROG

(MAGMA) [n*(n+3)/2+8: n in [0..60]]; // Vincenzo Librandi, Sep 16 2013

(PARI) a(n)=n*(n+3)/2+8 \\ Charles R Greathouse IV, Jun 16 2017

CROSSREFS

Cf. A167499.

Sequence in context: A203322 A120166 A030732 * A010916 A275627 A101764

Adjacent sequences:  A167484 A167485 A167486 * A167488 A167489 A167490

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Nov 07 2009

STATUS

approved

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Last modified April 21 15:55 EDT 2021. Contains 343156 sequences. (Running on oeis4.)