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A072259 a(n) = ((6*n+37)*4^n - 1)/3. 6
12, 57, 261, 1173, 5205, 22869, 99669, 431445, 1856853, 7951701, 33903957, 144004437, 609572181, 2572506453, 10826896725, 45455070549, 190410216789, 796000605525, 3321441375573, 13835521316181, 57541108520277, 238960527103317, 991026480502101 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Related to Collatz function (for n>0). All terms are divisible by 3.
LINKS
FORMULA
G.f.: 3*(4-17*x+12*x^2)/((1-x)*(1-4*x)^2). - Bruno Berselli, Dec 16 2011
E.g.f.: ((37 + 24*x)*exp(4*x) - exp(x))/3. - G. C. Greubel, Jan 14 2020
MAPLE
seq( ((6*n+37)*4^n -1)/3, n=0..30); # G. C. Greubel, Jan 14 2020
MATHEMATICA
LinearRecurrence[{9, -24, 16}, {12, 57, 261}, 30] (* Harvey P. Dale, Mar 10 2018 *)
PROG
(PARI) a(n)=((6*n+37)*4^n-1)/3 \\ Charles R Greathouse IV, Oct 07 2015
(Magma) [((6*n+37)*4^n -1)/3: n in [0..30]]; // G. C. Greubel, Jan 14 2020
(Sage) [((6*n+37)*4^n -1)/3 for n in (0..30)] # G. C. Greubel, Jan 14 2020
(GAP) List([0..30], n-> ((6*n+37)*4^n -1)/3); # G. C. Greubel, Jan 14 2020
CROSSREFS
Sequence in context: A212065 A121693 A190297 * A272233 A283164 A242983
KEYWORD
nonn,easy
AUTHOR
N. Rathankar (rathankar(AT)yahoo.com), Jul 08 2002
EXTENSIONS
Edited and extended by Henry Bottomley, Aug 06 2002
More terms from Harvey P. Dale, Mar 10 2018
STATUS
approved

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Last modified February 24 02:58 EST 2024. Contains 370288 sequences. (Running on oeis4.)