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A081345 First row in maze arrangement of natural numbers A081344. 3
1, 4, 5, 16, 17, 36, 37, 64, 65, 100, 101, 144, 145, 196, 197, 256, 257, 324, 325, 400, 401, 484, 485, 576, 577, 676, 677, 784, 785, 900, 901, 1024, 1025, 1156, 1157, 1296, 1297, 1444, 1445, 1600, 1601, 1764, 1765, 1936, 1937, 2116, 2117, 2304, 2305, 2500 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

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

FORMULA

a(n) = n^2 + n + 1 - n*(-1)^n = n^2 + n + 1 + n*(-1)^(n+1).

a(2*n) = A053755(n), a(2*n+1) = 4 * A004120(n).

G.f.: (5*x^3-x^2+3*x+1)/((1-x)^3*(1+x)^2). [Colin Barker, Sep 03 2012]

MATHEMATICA

CoefficientList[Series[(5 x^3 - x^2 + 3 x + 1) / ((1 - x)^3 (1 + x)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 08 2013 *)

PROG

(MAGMA) [n^2+n+1-n*(-1)^n: n in [0..50]]; // Vincenzo Librandi, Aug 08 2013

CROSSREFS

Cf. A081346.

Sequence in context: A078713 A175263 A000695 * A137527 A024854 A025617

Adjacent sequences:  A081342 A081343 A081344 * A081346 A081347 A081348

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 19 2003

STATUS

approved

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Last modified January 22 08:43 EST 2018. Contains 298042 sequences.