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A155883 a(n) = 14*n^3 - 30*n^2 + 24*n - 7. 2
1, 33, 173, 505, 1113, 2081, 3493, 5433, 7985, 11233, 15261, 20153, 25993, 32865, 40853, 50041, 60513, 72353, 85645, 100473, 116921, 135073, 155013, 176825, 200593, 226401, 254333, 284473, 316905, 351713, 388981, 428793, 471233, 516385, 564333, 615161, 668953 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Previous name was: The sequence gives the three-dimensional forms of the centered hexagonal numbers. Two examples: its third term 173 is built 19 + 37 + 61 + 37 + 19 and its fourth term 505 is built 37 + 61 + 91 + 127 + 91 + 61 + 37.

The sequence's digital roots run through 1, 6, 2.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

David Z. Crookes, De Pulchritudine Numerorum Figuratorum (On the Beauty of Figurate Numbers), Mathematics in School (May, 1988), 38-39.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = 14*n^3 - 30*n^2 + 24*n - 7.

G.f.: x*(1+29*x+47*x^2+7*x^3)/(1-x)^4. [Colin Barker, Jun 16 2012]

a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - Vincenzo Librandi, Jun 30 2012

MATHEMATICA

CoefficientList[Series[(1+29*x+47*x^2+7*x^3)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 30 2012 *)

PROG

(MAGMA) I:=[1, 33, 173, 505]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]];  // Vincenzo Librandi, Jun 30 2012

CROSSREFS

Sequence in context: A172077 A180943 A113752 * A071914 A279867 A230650

Adjacent sequences:  A155880 A155881 A155882 * A155884 A155885 A155886

KEYWORD

nonn,easy,less

AUTHOR

David Z. Crookes, Jan 29 2009

EXTENSIONS

More terms from Colin Barker, Jun 16 2012

New name using explicit formula from Joerg Arndt, Jan 15 2021

STATUS

approved

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Last modified April 11 00:03 EDT 2021. Contains 342877 sequences. (Running on oeis4.)