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A195142 Concentric 10-gonal numbers. 14
0, 1, 10, 21, 40, 61, 90, 121, 160, 201, 250, 301, 360, 421, 490, 561, 640, 721, 810, 901, 1000, 1101, 1210, 1321, 1440, 1561, 1690, 1821, 1960, 2101, 2250, 2401, 2560, 2721, 2890, 3061, 3240, 3421, 3610, 3801, 4000, 4201, 4410, 4621, 4840, 5061, 5290 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also concentric decagonal numbers. Also sequence found by reading the line from 0, in the direction 0, 10,..., and the same line from 1, in the direction 1, 21,..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. Main axis, perpendicular to A028895 in the same spiral.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

FORMULA

G.f. -x*(1+8*x+x^2) / ( (1+x)*(x-1)^3 ). - R. J. Mathar, Sep 18 2011

a(n) = -a(n-1)+5*n^2-5*n+1, a(0)=0. - Vincenzo Librandi, Sep 27 2011

a(n) = a(-n) = (10*n^2+3*(-1)^n-3)/4.  a(n) = a(n-2)+10*(n-1). - Bruno Berselli, Sep 27 2011

a(0)=0, a(1)=1, a(2)=10, a(3)=21, a(n)=2*a(n-1)+0*a(n-2)-2*a(n-3)+a(n-4) [From Harvey P. Dale, Sep 29 2011]

MATHEMATICA

RecurrenceTable[{a[0]==0, a[1]==1, a[n]==a[n-2]+10(n-1)}, a[n], {n, 50}] (* or *) LinearRecurrence[{2, 0, -2, 1}, {0, 1, 10, 21}, 50] (* Harvey P. Dale, Sep 29 2011 *)

PROG

(MAGMA) [(10*n^2+3*(-1)^n-3)/4: n in [0..50]]; // Vincenzo Librandi, Sep 27 2011

(Haskell)

a195142 n = a195142_list !! n

a195142_list = scanl (+) 0 a090771_list

-- Reinhard Zumkeller, Jan 07 2012

CROSSREFS

Cf. A033583 and A069133 interleaved.

Cf. A032527, A032528, A077221, A195042, A195143, A195145, A195146, A195147, A195148, A195149.

Cf. A090771 (first differences).

Column 10 of A195040. - Omar E. Pol, Sep 28 2011

Sequence in context: A164714 A240536 A060852 * A256884 A089584 A192743

Adjacent sequences:  A195139 A195140 A195141 * A195143 A195144 A195145

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Sep 17 2011

STATUS

approved

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Last modified July 26 00:44 EDT 2017. Contains 289798 sequences.